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RAMANUJAN THETA-FUNCTION

  • Ramanujan theta function
  • Mathematical function

    mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties

    Ramanujan theta function

    Ramanujan_theta_function

  • Theta function
  • Special functions of several complex variables

    mathematics, theta functions are special functions of several complex variables. Fundamentally, they are a family of continuous functions which encode

    Theta function

    Theta function

    Theta_function

  • Srinivasa Ramanujan
  • Indian mathematician (1887–1920)

    unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas

    Srinivasa Ramanujan

    Srinivasa Ramanujan

    Srinivasa_Ramanujan

  • Rogers–Ramanujan identities
  • Mathematical identities related to integer partitions

    the following identities to the remaining Rogers–Ramanujan functions and to the Ramanujan theta function described above: S ( q ) = q 1 / 5 H ( − q ) G

    Rogers–Ramanujan identities

    Rogers–Ramanujan_identities

  • Triangular number
  • Figurate number

    the sum of triangular numbers are connected to theta functions, in particular the Ramanujan theta function. The number of line segments between closest

    Triangular number

    Triangular number

    Triangular_number

  • Jacobi elliptic functions
  • Mathematical function

    functions. Elliptic curve Schwarz–Christoffel mapping Carlson symmetric form Jacobi theta function Ramanujan theta function Dixon elliptic functions Abel

    Jacobi elliptic functions

    Jacobi_elliptic_functions

  • Mock modular form
  • Complex-differentiable part of a Maass wave function

    theta function is essentially a mock modular form of weight ⁠1/2⁠. The first examples of mock theta functions were described by Srinivasa Ramanujan in

    Mock modular form

    Mock_modular_form

  • Q-theta function
  • q-Pochhammer symbol. elliptic hypergeometric series Jacobi theta function Ramanujan theta function Gasper, George; Rahman, Mizan (2004). Basic Hypergeometric

    Q-theta function

    Q-theta_function

  • Partition function (number theory)
  • Number of partitions of an integer

    this function is an alternating sum of pentagonal number powers of its argument. Srinivasa Ramanujan first discovered that the partition function has nontrivial

    Partition function (number theory)

    Partition function (number theory)

    Partition_function_(number_theory)

  • Theta function (disambiguation)
  • Topics referred to by the same term

    1/2 Ramanujan theta function, f ( a , b ) {\displaystyle f(a,b)} Neville theta functions Riemann–Siegel theta function, θ ( t ) {\displaystyle \theta (t)}

    Theta function (disambiguation)

    Theta_function_(disambiguation)

  • Inverse trigonometric functions
  • Inverse functions of sin, cos, tan, etc.

    trigonometric functions. For example, if x = sin ⁡ θ {\displaystyle x=\sin \theta } , then d x / d θ = cos ⁡ θ = 1 − x 2 , {\textstyle dx/d\theta =\cos \theta ={\sqrt

    Inverse trigonometric functions

    Inverse trigonometric functions

    Inverse_trigonometric_functions

  • Ramanujan's lost notebook
  • Collection of Srinivasa Ramanujan's discoveries in mathematics

    was settled because Ramanujan's final letters to Hardy had referred to the discovery of what Ramanujan called mock theta functions, although without great

    Ramanujan's lost notebook

    Ramanujan's_lost_notebook

  • Weber modular function
  • connections and consistent notation with the Ramanujan G- and g-functions and the Jacobi theta functions, both of which conventionally uses the nome.

    Weber modular function

    Weber_modular_function

  • List of things named after Srinivasa Ramanujan
  • identity Ramanujan machine Ramanujan–Nagell equation Ramanujan–Peterssen conjecture Ramanujan–Soldner constant Ramanujan summation Ramanujan theta function Ramanujan

    List of things named after Srinivasa Ramanujan

    List_of_things_named_after_Srinivasa_Ramanujan

  • Ramanujan summation
  • Mathematical techniques for summing divergent infinite series

    Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to divergent infinite series. Although the Ramanujan

    Ramanujan summation

    Ramanujan_summation

  • Perimeter of an ellipse
  • define the function E ( x ) = ∫ 0 π / 2 1 − x sin 2 ⁡ θ   d θ , {\displaystyle E(x)=\int _{0}^{\pi /2}{\sqrt {1-x\sin ^{2}\theta }}\ d\theta ,} known as

    Perimeter of an ellipse

    Perimeter of an ellipse

    Perimeter_of_an_ellipse

  • Arithmetic function
  • Function whose domain is the positive integers

    Arithmetic functions are often extremely irregular (see table), but some of them have series expansions in terms of Ramanujan's sum. An arithmetic function a is

    Arithmetic function

    Arithmetic_function

  • Elliptic integral
  • Special function defined by an integral

    elliptic functions Jacobi theta function Meridian arc Pendulum period Ramanujan theta function Schwarz–Christoffel mapping Weierstrass's elliptic functions K

    Elliptic integral

    Elliptic_integral

  • Hardy–Ramanujan–Littlewood circle method
  • Technique in analytic number theory

    work of Hardy with Srinivasa Ramanujan a few years earlier, in 1916 and 1917, on the asymptotics of the partition function. It was taken up by many other

    Hardy–Ramanujan–Littlewood circle method

    Hardy–Ramanujan–Littlewood_circle_method

  • Rogers–Ramanujan continued fraction
  • Continued fraction closely related to the Rogers–Ramanujan identities

    related to the Rogers–Ramanujan identities. It can be evaluated explicitly for a broad class of values of its argument. Given the functions G ( q ) {\displaystyle

    Rogers–Ramanujan continued fraction

    Rogers–Ramanujan continued fraction

    Rogers–Ramanujan_continued_fraction

  • Gamma distribution
  • Probability distribution

    approximation of the median by comparing the median to Ramanujan's θ {\displaystyle \theta } function. Berg and Pedersen found more terms: ν ( α ) = α − 1

    Gamma distribution

    Gamma distribution

    Gamma_distribution

  • Elliptic hypergeometric series
  • Elliptic analog of hypergeometric series

    modified Jacobi theta function with argument x and nome p is defined by θ ( x ; p ) = ( x , p / x ; p ) ∞ {\displaystyle \displaystyle \theta (x;p)=(x,p/x;p)_{\infty

    Elliptic hypergeometric series

    Elliptic_hypergeometric_series

  • Floor and ceiling functions
  • Nearest integers from a number

    " Ramanujan, Question 723, Papers p. 332 Somu, Sai Teja; Kukla, Andrzej (2022). "On some generalizations to floor function identities of Ramanujan" (PDF)

    Floor and ceiling functions

    Floor and ceiling functions

    Floor_and_ceiling_functions

  • Dedekind eta function
  • Mathematical function

    Jacobi Theta function and ϑ 1 ( z | τ ) = − ϑ 11 ( z ; τ ) {\displaystyle \vartheta _{1}(z|\tau )=-\vartheta _{11}(z;\tau )} Because the eta function is easy

    Dedekind eta function

    Dedekind_eta_function

  • Pi
  • Number, approximately 3.14

    ⁠. An example is the Jacobi theta function θ ( z , τ ) = ∑ n = − ∞ ∞ e 2 π i n z   +   π i n 2 τ , {\displaystyle \theta (z,\tau )=\sum _{n=-\infty }^{\infty

    Pi

    Pi

  • Jacobi triple product
  • Mathematical identity found by Jacobi in 1829

    enjoys a particularly elegant form when expressed in terms of the Ramanujan theta function. For | a b | < 1 {\displaystyle |ab|<1} it can be written as ∑

    Jacobi triple product

    Jacobi_triple_product

  • Weierstrass elliptic function
  • Class of mathematical functions

    \eta } is the Dedekind eta function. For the Fourier coefficients of Δ {\displaystyle \Delta } , see Ramanujan tau function. e 1 {\displaystyle e_{1}}

    Weierstrass elliptic function

    Weierstrass elliptic function

    Weierstrass_elliptic_function

  • Infinite product
  • Mathematical concept

    result concerning infinite products is that every entire function f(z) (that is, every function that is holomorphic over the entire complex plane) can be

    Infinite product

    Infinite_product

  • List of formulae involving π
  • Uses of the constant

    Mathematical Society. ISBN 0-8218-3246-8. p. 112 Cooper, Shaun (2017). Ramanujan's Theta Functions (First ed.). Springer. ISBN 978-3-319-56171-4. (page 647) Euler

    List of formulae involving π

    List_of_formulae_involving_π

  • Stirling's approximation
  • Approximation for factorials

    } An alternative approximation for the gamma function stated by Srinivasa Ramanujan in Ramanujan's lost notebook is Γ ( 1 + x ) ≈ π ( x e ) x ( 8 x

    Stirling's approximation

    Stirling's approximation

    Stirling's_approximation

  • Particular values of the gamma function
  • Mathematical constants

    related results". The Ramanujan Journal. 35 (1): 21–110. doi:10.1007/s11139-013-9528-5. ISSN 1572-9303. Weisstein, Eric W. "Gamma Function". MathWorld. Raimundas

    Particular values of the gamma function

    Particular_values_of_the_gamma_function

  • Riemann zeta function
  • Analytic function in mathematics

    Particular values of the Riemann zeta function Prime zeta function Renormalization Riemann–Siegel theta function ZetaGrid "Jupyter Notebook Viewer". Nbviewer

    Riemann zeta function

    Riemann zeta function

    Riemann_zeta_function

  • Θ10
  • "generalized Ramanujan conjecture" for (quasi-) split groups", in Borel, Armand; Casselman, W. (eds.), Automorphic forms, representations and L-functions (Proc

    Θ10

    Θ10

  • List of Brahmins
  • List of notable people who belong to the Brahmin caste

    Srinivasa Ramanujan, Greatest Indian mathematician who compiled Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions and

    List of Brahmins

    List_of_Brahmins

  • J-invariant
  • Modular function in mathematics

    found in Ramanujan's theory of elliptic functions to alternative bases. The inversion is applied in high-precision calculations of elliptic function periods

    J-invariant

    J-invariant

    J-invariant

  • Lambert series
  • Mathematical term

    }q^{n^{2}}} with the sum on the right similar to the Ramanujan theta function, or Jacobi theta function ϑ 3 ( q ) {\displaystyle \vartheta _{3}(q)} . Note

    Lambert series

    Lambert series

    Lambert_series

  • List of Indian inventions and discoveries
  • Indian inventions

    Kesavan Raghavan Nair in 1939. Ramanujan theta function, Ramanujan prime, Ramanujan summation, Ramanujan graph and Ramanujan's sum – Discovered by the Indian

    List of Indian inventions and discoveries

    List_of_Indian_inventions_and_discoveries

  • Undefined (mathematics)
  • Expression which is not assigned an interpretation

    However, Ramanujan summation is useful for modelling a number of real-world phenomena, including the Casimir effect and bosonic string theory. A function may

    Undefined (mathematics)

    Undefined_(mathematics)

  • Modular form
  • Analytic function on the upper half-plane with a certain behavior under the modular group

    essentially Ramanujan's mock theta functions. Groups which are not subgroups of SL(2, Z) can be considered. Hilbert modular forms are functions in n variables

    Modular form

    Modular_form

  • Sander P. Zwegers
  • Dutch mathematician (born 1975)

    for making a connection between Maass forms and Srinivasa Ramanujan's mock theta functions in 2002. He was born in Oosterhout. After a period at the Max-Planck

    Sander P. Zwegers

    Sander_P._Zwegers

  • Eisenstein series
  • Series representing modular forms

    on modular invariants provides expressions for these two functions in terms of theta functions. Any holomorphic modular form for the modular group can

    Eisenstein series

    Eisenstein_series

  • List of eponyms of special functions
  • Jackson integral Carl Gustav Jakob Jacobi: Jacobi polynomial, Jacobi theta function Joseph Marie Kampe de Feriet (1893–1982): Kampe de Feriet hypergeometric

    List of eponyms of special functions

    List_of_eponyms_of_special_functions

  • Poisson distribution
  • Discrete probability distribution

    v)=\exp[(\theta _{1}-\theta _{12})(u-1)+(\theta _{2}-\theta _{12})(v-1)+\theta _{12}(uv-1)]} with θ 1 , θ 2 > θ 12 > 0 {\displaystyle \theta _{1},\theta _{2}>\theta

    Poisson distribution

    Poisson distribution

    Poisson_distribution

  • Euler's constant
  • Difference between logarithm and harmonic series

    generalized-Euler-constant function and its derivative, arXiv:0808.0410 Berndt, Bruce C. (January 2008). "A fragment on Euler's constant in Ramanujan's lost notebook"

    Euler's constant

    Euler's constant

    Euler's_constant

  • Lemniscate elliptic functions
  • Mathematical functions

    exponential function. An alternative way of expressing the lemniscate functions as a ratio of entire functions involves the theta functions (see Lemniscate

    Lemniscate elliptic functions

    Lemniscate elliptic functions

    Lemniscate_elliptic_functions

  • Modular lambda function
  • Symmetric holomorphic function

    )=k^{2}(\tau )} . In terms of the Dedekind eta function η ( τ ) {\displaystyle \eta (\tau )} and theta functions, λ ( τ ) = ( 2 η ( τ 2 ) η 2 ( 2 τ ) η 3 (

    Modular lambda function

    Modular lambda function

    Modular_lambda_function

  • Riemann hypothesis
  • Conjecture on zeros of the zeta function

    finite graph is a Ramanujan graph, a mathematical model of efficient communication networks, if and only if its Ihara zeta function satisfies the analogue

    Riemann hypothesis

    Riemann hypothesis

    Riemann_hypothesis

  • Jackson q-Bessel function
  • S2CID 119142457 Ismail, M. E. H.; Zhang, R. (2018b), "q-Bessel Functions and Rogers-Ramanujan Type Identities", Proceedings of the American Mathematical Society

    Jackson q-Bessel function

    Jackson_q-Bessel_function

  • Generalized Riemann hypothesis
  • Mathematical conjecture about zeros of L-functions

    for much more general L-functions than Dedekind zeta functions lie on critical lines. One example can be Ramanujan L-function related to modular form

    Generalized Riemann hypothesis

    Generalized_Riemann_hypothesis

  • Hurwitz zeta function
  • Special function in mathematics

    representation along with the residue theorem. A second proof uses a theta function identity, or equivalently Poisson summation. These proofs are analogous

    Hurwitz zeta function

    Hurwitz zeta function

    Hurwitz_zeta_function

  • Nome (mathematics)
  • Special mathematical function

    description of the elliptic functions, especially in the description of the modular identity of the Jacobi theta function, the Hermite elliptic transcendents

    Nome (mathematics)

    Nome_(mathematics)

  • Timeline of Indian innovation
  • Landau–Ramanujan constant, Mock theta functions, Ramanujan conjecture, Ramanujan prime, Ramanujan–Soldner constant, Ramanujan theta function, Ramanujan's sum

    Timeline of Indian innovation

    Timeline_of_Indian_innovation

  • Fransén–Robinson constant
  • Mathematical constant

    /2}e^{\pi \tan \theta }e^{-e^{\pi \tan \theta }}\,d\theta .} The Fransén–Robinson constant can also be expressed using the Mittag-Leffler function as the limit

    Fransén–Robinson constant

    Fransén–Robinson constant

    Fransén–Robinson_constant

  • List of eponyms (L–Z)
  • Srinivasa Ramanujan, Indian mathematician – Ramanujan prime, Ramanujan theta function, Ramanujan's sum, Ramanujan's master theorem, Landau–Ramanujan constant

    List of eponyms (L–Z)

    List_of_eponyms_(L–Z)

  • Gelfond's constant
  • Constant e raised to the power of pi

     Doman in September 2023 and is a result of a sum related to Jacobi theta functions as follows: ∑ k = 1 ∞ ( 8 π k 2 − 2 ) e − π k 2 = 1. {\displaystyle

    Gelfond's constant

    Gelfond's_constant

  • Q-Pochhammer symbol
  • Concept in combinatorics (part of mathematics)

    Pentagonal number theorem q-derivative q-theta function q-Vandermonde identity Rogers–Ramanujan identities Rogers–Ramanujan continued fraction Berndt, B. C. "What

    Q-Pochhammer symbol

    Q-Pochhammer_symbol

  • Eric Harold Neville
  • English mathematician

    'Srinivasa Ramanujan" Nature 149:292. 1944: Jacobian Elliptic Functions, Clarendon Press via Internet Archive Neville's algorithm Neville theta functions Senechal

    Eric Harold Neville

    Eric_Harold_Neville

  • Pythagorean theorem
  • Relation between sides of a right triangle

    \theta _{1}\cos \theta _{2}+\sin \theta _{1}\sin \theta _{2}\right)\\&=r_{1}^{2}+r_{2}^{2}-2r_{1}r_{2}\cos \left(\theta _{1}-\theta

    Pythagorean theorem

    Pythagorean theorem

    Pythagorean_theorem

  • Tau
  • Nineteenth letter in the Greek alphabet

    chronic traumatic encephalopathy Divisor function in number theory, also denoted d or σ0 Ramanujan tau function Golden ratio (1.618...), although φ (phi)

    Tau

    Tau

  • Umbral
  • Topics referred to by the same term

    moonshine, a mysterious connection between Niemeier lattices and Ramanujan's mock theta functions Francisco Umbral (1932–2007), Spanish journalist, novelist

    Umbral

    Umbral

  • Umbral moonshine
  • Topic in group theory and harmonic analysis (Niemeier lattice-mock theta connection)

    moonshine is a mysterious connection between Niemeier lattices and Ramanujan's mock theta functions. It is a generalization of the Mathieu moonshine phenomenon

    Umbral moonshine

    Umbral moonshine

    Umbral_moonshine

  • Mellin transform
  • Mathematical operation

    {\displaystyle F(s,\theta )=A(s){\frac {\sin(s(\theta _{0}-\theta ))}{\sin(2\theta _{0}s)}}+B(s){\frac {\sin(s(\theta _{0}+\theta ))}{\sin(2\theta _{0}s)}}} Now

    Mellin transform

    Mellin_transform

  • Rankin–Selberg method
  • constructed his zeta function as the Mellin transform of Jacobi's theta function. Riemann used asymptotics of the theta function to obtain the analytic

    Rankin–Selberg method

    Rankin–Selberg_method

  • Polylogarithm
  • Special mathematical function

    (1989). "The dilogarithm function in geometry and number theory". Number Theory and Related Topics: papers presented at the Ramanujan Colloquium, Bombay, 1988

    Polylogarithm

    Polylogarithm

    Polylogarithm

  • Greek letters used in mathematics, science, and engineering
  • Symbols for constants, special functions

    correlation coefficient, a measure of rank correlation in statistics Ramanujan's tau function in number theory shear stress in continuum mechanics a type variable

    Greek letters used in mathematics, science, and engineering

    Greek_letters_used_in_mathematics,_science,_and_engineering

  • Kathrin Bringmann
  • German mathematician (born 1977)

    Germany, who has made fundamental contributions to the theory of mock theta functions. Kathrin Bringmann was born on 8 May 1977, in Muenster, Germany. She

    Kathrin Bringmann

    Kathrin Bringmann

    Kathrin_Bringmann

  • Selberg class
  • Axiomatic definition of a class of L-functions

    is entire function in S, then F ( s + i t ) {\textstyle F(s+it)} for t ∈ R {\textstyle t\in \mathbb {R} } is also in S. From the Ramanujan conjecture

    Selberg class

    Selberg class

    Selberg_class

  • Poisson summation formula
  • Equation in Fourier analysis

    to prove the functional equation for the theta function. Poisson's summation formula appears in Ramanujan's notebooks and can be used to prove some of

    Poisson summation formula

    Poisson_summation_formula

  • Ellipse
  • Plane curve

    \int _{0}^{\pi /2}{\sqrt {1-e^{2}\sin ^{2}\theta }}\ d\theta } which is in general not an elementary function. The circumference of the ellipse may be evaluated

    Ellipse

    Ellipse

    Ellipse

  • Automorphic form
  • Type of generalization of periodic functions in Euclidean space

    symplectic group, arose naturally from considering moduli spaces and theta functions. The post-war interest in several complex variables made it natural

    Automorphic form

    Automorphic_form

  • G. N. Watson
  • English mathematician (1886–1965)

    years on Ramanujan's formulae in the area of modular equations, mock theta functions and q-series, and for some time looked after Ramanujan's lost notebook

    G. N. Watson

    G._N._Watson

  • Area of a circle
  • Concept in geometry

    {r^{2}\left(1-\sin ^{2}\theta \right)}}\cdot r\cos \theta \,d\theta \\[5pt]&=2r^{2}\int _{0}^{\frac {\pi }{2}}\cos ^{2}\theta \,d\theta \\[5pt]&={\frac {\pi

    Area of a circle

    Area_of_a_circle

  • Dixon elliptic functions
  • & P. Flajolet (2010) “Pseudo-factorials, elliptic functions, and continued fractions” The Ramanujan journal 21(1), 71–97. https://arxiv.org/pdf/0901.1379

    Dixon elliptic functions

    Dixon elliptic functions

    Dixon_elliptic_functions

  • Basel problem
  • Sum of inverse squares of natural numbers

    archived from the original (PDF) on 2011-07-06 Berndt, Bruce C. (1989), Ramanujan's Notebooks: Part II, Springer-Verlag, p. 150, ISBN 978-0-387-96794-3 An

    Basel problem

    Basel problem

    Basel_problem

  • List of mathematical constants
  • MathWorld. Weisstein, Eric W. "Landau-Ramanujan Constant". MathWorld. Weisstein, Eric W. "Nielsen-Ramanujan Constants". MathWorld. Weisstein, Eric W

    List of mathematical constants

    List_of_mathematical_constants

  • Yifeng Liu
  • Chinese professor of mathematics

    contributions span a wide spectrum of topics such as arithmetic theta lifts and derivatives of L-functions, the Gan–Gross–Prasad conjecture and its arithmetic counterpart

    Yifeng Liu

    Yifeng Liu

    Yifeng_Liu

  • Quintuple product identity
  • Infinite product identity introduced by Watson

    W. N. (1951), "On the simplification of some identities of the Rogers-Ramanujan type", Proceedings of the London Mathematical Society, Third Series, 1:

    Quintuple product identity

    Quintuple_product_identity

  • Leech lattice
  • 24-dimensional repeating pattern of points

    \sigma _{11}(n)} is the divisor function for exponent 11, and τ ( n ) {\displaystyle \tau (n)} is the Ramanujan tau function. It follows that for m ≥ 1, the

    Leech lattice

    Leech_lattice

  • Madhava of Sangamagrama
  • Indian mathematician and astronomer (1340–1425)

    ⋯ {\displaystyle r\theta ={\frac {r\sin \theta }{\cos \theta }}-(1/3)\,r\,{\frac {\left(\sin \theta \right)^{3}}{\left(\cos \theta \right)^{3}}}+(1/5)\

    Madhava of Sangamagrama

    Madhava_of_Sangamagrama

  • Abel–Plana formula
  • Summation formula in Mathematics

    (x+1)=\operatorname {Li} _{-x}\left(e^{-1}\right)+\theta (x)} where Γ ( x ) {\displaystyle \Gamma (x)} is the gamma function, Li s ⁡ ( z ) {\displaystyle \operatorname

    Abel–Plana formula

    Abel–Plana_formula

  • Proof of Bertrand's postulate
  • Solved prime-number problem

    proven by Chebyshev, and a shorter but also advanced proof was given by Ramanujan. The following elementary proof was published by Paul Erdős in 1932, as

    Proof of Bertrand's postulate

    Proof_of_Bertrand's_postulate

  • Touchard polynomials
  • Sequence of polynomials

    }e^{x{\bigl (}e^{\cos(\theta )}\cos(\sin(\theta ))-1{\bigr )}}\cos {\bigl (}xe^{\cos(\theta )}\sin(\sin(\theta ))-n\theta {\bigr )}\,d\theta \,.} Bell polynomials

    Touchard polynomials

    Touchard polynomials

    Touchard_polynomials

  • Leila Bram
  • American mathematician

    from it) became one of only three works to study the mock theta functions between Ramanujan in the 1920s and the work of George Andrews beginning in 1966

    Leila Bram

    Leila_Bram

  • Nayandeep Deka Baruah
  • Indian mathematician and professor (born 1972)

    his Ph.D. thesis was Contributions to Ramanujan's Schlafli-type Modular Equations, Class Invariants, Theta-functions, and Continued Fractions. Following

    Nayandeep Deka Baruah

    Nayandeep Deka Baruah

    Nayandeep_Deka_Baruah

  • Computational complexity of mathematical operations
  • Algorithmic runtime requirements for common math procedures

    (1988). "Approximations and complex multiplication according to Ramanujan". Ramanujan revisited: Proceedings of the Centenary Conference. Academic Press

    Computational complexity of mathematical operations

    Computational complexity of mathematical operations

    Computational_complexity_of_mathematical_operations

  • The Dynamics of an Asteroid
  • Fictional book from the Sherlock Holmes book series

    genius Ramanujan. Scribner. p. 168. ISBN 978-0-671-75061-9. Watson, G. N. (2001). "The final problem: an account of the mock theta functions". Ramanujan: essays

    The Dynamics of an Asteroid

    The_Dynamics_of_an_Asteroid

  • Circumference
  • Perimeter of a circle or ellipse

    S2CID 126427943. Almkvist, Gert; Berndt, Bruce (1988), "Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, π, and the Ladies Diary", American

    Circumference

    Circumference

    Circumference

  • Riesz function
  • Mathematical function

    Riesz function is defined on the strip − 1 < ℜ ( s ) < − 1 2 {\displaystyle -1<\Re (s)<-{\frac {1}{2}}} . On this strip, we have (cf. Ramanujan's master

    Riesz function

    Riesz function

    Riesz_function

  • Maass wave form
  • Complex-valued smooth functions of the upper half plane (harmonic analysis topic)

    {\displaystyle k_{\theta }={\begin{pmatrix}\cos(\theta )&-\sin(\theta )\\\sin(\theta )&\cos(\theta )\\\end{pmatrix}}\in SO(2),\theta \in \mathbb {R} .}

    Maass wave form

    Maass_wave_form

  • Transcendental number
  • In mathematics, a non-algebraic number

    73.140. ISSN 0386-2194. Bertrand, Daniel (1997). "Theta functions and transcendence". The Ramanujan Journal. 1 (4): 339–350. doi:10.1023/A:1009749608672

    Transcendental number

    Transcendental_number

  • Timeline of number theory
  • Ramanujan develops over 3000 theorems, including properties of highly composite numbers, the partition function and its asymptotics, and mock theta functions

    Timeline of number theory

    Timeline_of_number_theory

  • Supergolden ratio
  • Number, approximately 1.46557

    = xn/m German Wikipedia has a table of analytical values of the Ramanujan G-function [de] for odd arguments below 47. Sloane, N. J. A. (ed.). "Sequence

    Supergolden ratio

    Supergolden ratio

    Supergolden_ratio

  • Stieltjes constants
  • Constants in the zeta function's Laurent series expansion

    infinite series are given in works of Jensen, Franel, Hermite, Hardy, Ramanujan, Ainsworth, Howell, Coppo, Connon, Coffey, Choi, Blagouchine and some

    Stieltjes constants

    Stieltjes constants

    Stieltjes_constants

  • Grahalaghava
  • 16th-century Sanskrit treatise on astronomy

    well known result sin ⁡ θ ≈ θ {\displaystyle \sin \theta \approx \theta } when θ {\displaystyle \theta } is in radians and is small. Full text of the work

    Grahalaghava

    Grahalaghava

  • Four exponentials conjecture
  • JSTOR 1990319. MR 0011087. Bertrand, Daniel (1997). "Theta functions and transcendence". The Ramanujan Journal. 1 (4): 339–350. doi:10.1023/A:1009749608672

    Four exponentials conjecture

    Four_exponentials_conjecture

  • Henry F. Baker
  • British mathematician (1866–1956)

    the theory of the theta functions (Cambridge: The University Press, 1897) An introduction to the theory of multiply periodic functions (Cambridge: The University

    Henry F. Baker

    Henry F. Baker

    Henry_F._Baker

  • Complex multiplication
  • Theory of a class of elliptic curves

    38, 495–512, 1974. English translation in Math. USSR 8, 501–518, 1974. Ramanujan Constant – from Wolfram MathWorld Silverman 1986, p. 339. Silverman 1994

    Complex multiplication

    Complex_multiplication

  • Anatoly Karatsuba
  • Russian mathematician (1937–2008)

    Applying his p {\displaystyle p} -adic form of the Hardy-Littlewood-Ramanujan-Vinogradov method to estimating trigonometric sums, in which the summation

    Anatoly Karatsuba

    Anatoly Karatsuba

    Anatoly_Karatsuba

  • Nonparametric skew
  • Statistical quantity

    Choi KP (1994) "On the medians of Gamma distributions and an equation of Ramanujan". Proc Amer Math Soc 121 (1) 245–251 Pearson K (1895) Contributions to

    Nonparametric skew

    Nonparametric_skew

  • Almost integer
  • Any number that is not an integer but is very close to one

    99791\,89\ldots } This can be explained using a sum related to Jacobi theta functions as follows: ∑ k = 1 ∞ ( 8 π k 2 − 2 ) e − π k 2 = 1. {\displaystyle

    Almost integer

    Almost integer

    Almost_integer

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  • Thea
  • Girl/Female

    Greek American

    Thea

    Goddess; godly. Also as abbreviation of names like Althea and Dorothea. The mythological Thea was...

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  • Boy/Male

    Hindu, Indian

    Ramanujam

    Name of Brother of Lord Rama

    Ramanujam

  • Theja
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    Hindu

    Theja

    Radiant

    Theja

  • THERA
  • Female

    Spanish

    THERA

     Pet form of Spanish Theresa, THERA means "harvester." Compare with another form of Thera.

    THERA

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    Hindu

    Ramanuja

    Born after Rama i.e. Lakshman (Younger brother of Rama)

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  • Female

    English

    THEDA

    Pet form of English Theodora, THEDA means "gift of God."

    THEDA

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  • Female

    English

    THEA

     Pet form of English Theodora, THEA means "gift of God." Compare with another form of Thea.

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    Hindu

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    He was a saint

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    Russian American Greek

    Theda

    God's gift.

    Theda

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  • Female

    Greek

    THERA

    (Θήρα) Greek name THERA means "lustrous." In mythology, this is the name of one of Amphion's seven daughters. Compare with another form of Thera.

    THERA

  • RHETA
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    English

    RHETA

    English variant spelling of Spanish Rita, RHETA means "pearl." 

    RHETA

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    Hindu, Indian

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    Lighting

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    Greek

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     Short form of Greek and Latin Dorothea, THEA means "gift of God." Compare with another form of Thea.

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    Quick

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    Untamed.

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    Hindu, Indian

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    Name of Lord Rama who is a King

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    Speaker.

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    Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu

    Ramanuja

    Lord Krishna; Born After Rama; Lakshman

    Ramanuja

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  • Girl/Female

    Egyptian

    Thema

    Queen.

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    American, Australian, British, Christian, English, German, Greek

    Theda

    Gift of God; Supreme Gift

    Theda

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Online names & meanings

  • Alyaan
  • Girl/Female

    Arabic, Gujarati, Indian, Kannada, Muslim

    Alyaan

    Headstrong; Bible; Ladder

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    Italian

    FIAMMETTA

    Italian name composed of the word fiamma "fire" and a diminutive suffix, FIAMMETTA means "little fire."

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    American, British, Christian, English

    Kemp

    Warrior; Fighter; Champion

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    Indian, Tamil

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    Bird

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    Arabic, Australian, Muslim

    AbdulNasser

    Servant of the Victorious One

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    Divyans

    Love; Lord

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    Strength

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    Calm and peaceful, Derived from Mary

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    Cherished. Famous bearers: British pop star David Bowie, American talk-show host David Letterman.

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    Tamil

    Sooryakanth | ஸூர்யகாஂத

    Effulgent like Sun, A kind of flower

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RAMANUJAN THETA-FUNCTION

  • Functionless
  • a.

    Destitute of function, or of an appropriate organ. Darwin.

  • Functionary
  • n.

    One charged with the performance of a function or office; as, a public functionary; secular functionaries.

  • Theca
  • n.

    A sheath; a case; as, the theca, or cell, of an anther; the theca, or spore case, of a fungus; the theca of the spinal cord.

  • Theta
  • n.

    A letter of the Greek alphabet corresponding to th in English; -- sometimes called the unlucky letter, from being used by the judges on their ballots in passing condemnation on a prisoner, it being the first letter of the Greek qa`natos, death.

  • Theca
  • n.

    The more or less cuplike calicle of a coral.

  • Camellia
  • n.

    An Asiatic genus of small shrubs, often with shining leaves and showy flowers. Camellia Japonica is much cultivated for ornament, and C. Sassanqua and C. oleifera are grown in China for the oil which is pressed from their seeds. The tea plant is now referred to this genus under the name of Camellia Thea.

  • Thecae
  • pl.

    of Theca

  • Thea
  • n.

    A genus of plants found in China and Japan; the tea plant.

  • Yuga
  • n.

    Any one of the four ages, Krita, or Satya, Treta, Dwapara, and Kali, into which the Hindoos divide the duration or existence of the world.

  • Theca
  • n.

    The wall forming a calicle of a coral.

  • Moment
  • n.

    A minute portion of time; a point of time; an instant; as, at thet very moment.

  • Functionaries
  • pl.

    of Functionary

  • Urn
  • n.

    A hollow body shaped like an urn, in which the spores of mosses are contained; a spore case; a theca.

  • Thecal
  • a.

    Of or pertaining to a theca; as, a thecal abscess.

  • Vagina
  • n.

    A sheath; a theca; as, the vagina of the portal vein.

  • Tea
  • n.

    The prepared leaves of a shrub, or small tree (Thea, / Camellia, Chinensis). The shrub is a native of China, but has been introduced to some extent into some other countries.

  • Pyxidium
  • n.

    The theca of mosses.

  • Theca
  • n.

    The chitinous cup which protects the hydranths of certain hydroids.

  • Functionally
  • adv.

    In a functional manner; as regards normal or appropriate activity.

  • Thecaphore
  • n.

    A surface or organ bearing a theca, or covered with thecae.