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INCOMPLETE GAMMA-FUNCTION

  • Incomplete gamma function
  • Types of special mathematical functions

    In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems

    Incomplete gamma function

    Incomplete gamma function

    Incomplete_gamma_function

  • Beta function
  • Mathematical function

    the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial

    Beta function

    Beta function

    Beta_function

  • Gamma function
  • Extension of the factorial function

    the gamma function (represented by ⁠ Γ {\displaystyle \Gamma } ⁠, capital Greek letter gamma) is the most common extension of the factorial function to

    Gamma function

    Gamma function

    Gamma_function

  • Gamma
  • Third letter of the Greek alphabet

    mathematics, the upper incomplete gamma function The Christoffel symbols in differential geometry In probability theory and statistics, the gamma distribution is

    Gamma

    Gamma

  • Incomplete Bessel K function/generalized incomplete gamma function
  • mathematicians defined this type incomplete-version of Bessel function or this type generalized-version of incomplete gamma function: K v ( x , y ) = ∫ 1 ∞ e

    Incomplete Bessel K function/generalized incomplete gamma function

    Incomplete_Bessel_K_function/generalized_incomplete_gamma_function

  • Generalized gamma distribution
  • Probability distribution

    the lower incomplete gamma function, and P ( ⋅ , ⋅ ) {\displaystyle P(\cdot ,\cdot )} denotes the regularized lower incomplete gamma function. The quantile

    Generalized gamma distribution

    Generalized gamma distribution

    Generalized_gamma_distribution

  • Inverse-gamma distribution
  • Two-parameter family of continuous probability distributions

    }{x}}\right)}{\Gamma (\alpha )}}=Q\left(\alpha ,{\frac {\beta }{x}}\right)\!} where the numerator is the upper incomplete gamma function and the denominator

    Inverse-gamma distribution

    Inverse-gamma distribution

    Inverse-gamma_distribution

  • Gamma distribution
  • Probability distribution

    {\gamma (\alpha ,\beta x)}{\Gamma (\alpha )}},} where γ ( α , β x ) {\displaystyle \gamma (\alpha ,\beta x)} is the lower incomplete gamma function. If

    Gamma distribution

    Gamma distribution

    Gamma_distribution

  • List of mathematical functions
  • function, Polygamma function Incomplete beta function Incomplete gamma function K-function Multivariate gamma function: A generalization of the Gamma

    List of mathematical functions

    List_of_mathematical_functions

  • Error function
  • Sigmoid shape special function

    [further explanation needed] In terms of the regularized gamma function P and the incomplete gamma function, erf ⁡ ( x ) = sgn ⁡ ( x ) ⋅ P ( 1 2 , x 2 ) = sgn

    Error function

    Error function

    Error_function

  • Incomplete polylogarithm
  • {z^{k}}{k^{s}}}~{\frac {\Gamma (s,kb)}{\Gamma (s)}}} where Γ(s) is the gamma function and Γ(s,x) is the upper incomplete gamma function. Since Γ(s,0)=Γ(s),

    Incomplete polylogarithm

    Incomplete_polylogarithm

  • Mittag-Leffler function
  • Mathematical function

    {\gamma (1-{\frac {n}{p}},z)}{\Gamma (1-{\frac {n}{p}})}}{\bigg ]}} where γ ( x , y ) {\displaystyle \gamma (x,y)} is the incomplete gamma function. The

    Mittag-Leffler function

    Mittag-Leffler function

    Mittag-Leffler_function

  • Logarithmic integral function
  • Special function defined by an integral

    π ) {\displaystyle -(\Gamma (0,-\ln 2)+i\,\pi )} where Γ ( a , x ) {\displaystyle \Gamma (a,x)} is the incomplete gamma function. It must be understood

    Logarithmic integral function

    Logarithmic integral function

    Logarithmic_integral_function

  • Polylogarithm
  • Special mathematical function

    t-t\ln z)}{(1+t^{2})^{s/2}(e^{2\pi t}-1)}}dt} where Γ is the upper incomplete gamma-function. All (but not part) of the ln(z) in this expression can be replaced

    Polylogarithm

    Polylogarithm

    Polylogarithm

  • Salem Hanna Khamis
  • Palestinian statistician and UN official (1919–2005)

    theory and the tabulation of the Incomplete gamma function, where he wrote the book “Tables of the Incomplete Gamma Function Ratio”.[citation needed] He contributed

    Salem Hanna Khamis

    Salem_Hanna_Khamis

  • Z function
  • Mathematical function

    using the incomplete gamma function. If Q ( a , z ) = Γ ( a , z ) Γ ( a ) = 1 Γ ( a ) ∫ z ∞ u a − 1 e − u d u {\displaystyle Q(a,z)={\frac {\Gamma (a,z)}{\Gamma

    Z function

    Z function

    Z_function

  • Confluent hypergeometric function
  • Solution of a confluent hypergeometric equation

    polynomials Incomplete gamma function Laguerre polynomials Parabolic cylinder function (or Weber function) Poisson–Charlier function Toronto functions Whittaker

    Confluent hypergeometric function

    Confluent hypergeometric function

    Confluent_hypergeometric_function

  • Luminosity function (astronomy)
  • Astronomical measure

    Schechter function with α = − 1 {\displaystyle \alpha =-1} is said to be flat. Integrals of the Schechter function can be expressed via the incomplete gamma function

    Luminosity function (astronomy)

    Luminosity_function_(astronomy)

  • Binomial coefficient
  • Number of subsets of a given size

    generalized to two real or complex valued arguments using the gamma function or beta function via ( x y ) = Γ ( x + 1 ) Γ ( y + 1 ) Γ ( x − y + 1 ) = 1 (

    Binomial coefficient

    Binomial coefficient

    Binomial_coefficient

  • Expected shortfall
  • Risk measure estimating the average loss in the worst tail of the distribution

    }{1-\alpha }}\Gamma \left(1+{\frac {1}{k}},-\ln(1-\alpha )\right)} , where Γ ( s , x ) {\displaystyle \Gamma (s,x)} is the upper incomplete gamma function. If the

    Expected shortfall

    Expected_shortfall

  • Marcum Q-function
  • Function in statistics

    The generalized Marcum Q function of order ν > 0 {\displaystyle \nu >0} can be represented using incomplete Gamma function as Q ν ( a , b ) = 1 − e −

    Marcum Q-function

    Marcum_Q-function

  • Generalized hypergeometric function
  • Family of power series in mathematics

    yields many interesting series in mathematics, for example the incomplete gamma function has the asymptotic expansion Γ ( a , z ) ∼ z a − 1 e − z ( 1 +

    Generalized hypergeometric function

    Generalized hypergeometric function

    Generalized_hypergeometric_function

  • Derangement
  • Permutation of the elements of a set in which no element appears in its original position

    {\Gamma (n+1,-1)}{e}}=\int _{0}^{\infty }(x-1)^{n}e^{-x}dx} where Γ ( s , x ) {\displaystyle \Gamma (s,x)} is the upper incomplete gamma function. It

    Derangement

    Derangement

    Derangement

  • Poisson distribution
  • Discrete probability distribution

    using the lgamma function in the C standard library (C99 version) or R, the gammaln function in MATLAB or SciPy, or the log_gamma function in Fortran 2008

    Poisson distribution

    Poisson distribution

    Poisson_distribution

  • L-function
  • Meromorphic function on the complex plane

    {s+\kappa _{j}}{2}}\right)} where Γ {\displaystyle \textstyle \Gamma } denotes the gamma function, π {\displaystyle \textstyle \pi } denotes the automorphic

    L-function

    L-function

    L-function

  • Exponential integral
  • Special function defined by an integral

    special case of the upper incomplete gamma function: E n ( x ) = x n − 1 Γ ( 1 − n , x ) . {\displaystyle E_{n}(x)=x^{n-1}\Gamma (1-n,x).} The generalized

    Exponential integral

    Exponential integral

    Exponential_integral

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

    essentially the incomplete gamma function. The integral converges whenever g has a zero at the cusp i∞, and the incomplete gamma function can be extended

    Mock modular form

    Mock_modular_form

  • List of integrals of exponential functions
  • j-1}&{\text{otherwise}}\end{cases}}} and Γ(x,y) is the upper incomplete gamma function. ∫ 1 a e λ x + b d x = x b − 1 b λ ln ⁡ ( a e λ x + b ) {\displaystyle

    List of integrals of exponential functions

    List_of_integrals_of_exponential_functions

  • Elliptic integral
  • Special function defined by an integral

    Historically, elliptic functions were discovered as inverse functions of elliptic integrals. Incomplete elliptic integrals are functions of two arguments;

    Elliptic integral

    Elliptic_integral

  • Incomplete Fermi–Dirac integral
  • {\displaystyle \Gamma (s,y)} is the upper incomplete gamma function. Since Γ ( s , 0 ) = Γ ( s ) {\displaystyle \Gamma (s,0)=\Gamma (s)} , it follows that: F j ⁡

    Incomplete Fermi–Dirac integral

    Incomplete_Fermi–Dirac_integral

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

    optical mode in a waveguide the gamma function, a generalization of the factorial the upper incomplete gamma function the modular group, the group of

    Greek letters used in mathematics, science, and engineering

    Greek_letters_used_in_mathematics,_science,_and_engineering

  • Fresnel integral
  • Special function defined by an integral

    {x^{m+nk+1}}{k!}}} is a confluent hypergeometric function and also an incomplete gamma function ∫ x m e i x n d x = x m + 1 m + 1 1 F 1 ( m + 1 n 1

    Fresnel integral

    Fresnel integral

    Fresnel_integral

  • Chi-squared distribution
  • Probability distribution and special case of gamma distribution

    \gamma (s,t)} is the lower incomplete gamma function and P ( s , t ) {\textstyle P(s,t)} is the regularized gamma function. In a special case of k = 2

    Chi-squared distribution

    Chi-squared distribution

    Chi-squared_distribution

  • Boundary layer
  • Layer of fluid in the immediate vicinity of a bounding surface

    temperature at any point in the fluid, can be expressed as an incomplete gamma function. Schlichting proposed an equivalent substitution that reduces

    Boundary layer

    Boundary layer

    Boundary_layer

  • Combinatorics
  • Branch of discrete mathematics

    combinatorics, which uses explicit combinatorial formulae and generating functions to describe the results, analytic combinatorics aims at obtaining asymptotic

    Combinatorics

    Combinatorics

  • Gautschi's inequality
  • mathematics, Gautschi's inequality is an inequality for ratios of gamma functions. It is named after Walter Gautschi. Let x {\displaystyle x} be a positive

    Gautschi's inequality

    Gautschi's_inequality

  • List of factorial and binomial topics
  • identities Hypergeometric series Incomplete beta function Incomplete gamma function Jordan–Pólya number Kempner function Lah number Lanczos approximation

    List of factorial and binomial topics

    List_of_factorial_and_binomial_topics

  • Pareto distribution
  • Probability distribution

    (-ix_{\mathrm {m} }t)^{\alpha }\Gamma (-\alpha ,-ix_{\mathrm {m} }t),} where Γ(a, x) is the incomplete gamma function. The parameters may be solved for

    Pareto distribution

    Pareto distribution

    Pareto_distribution

  • Tail value at risk
  • Measure giving the average loss beyond a specified Value-at-Risk level

    }{1-\alpha }}\Gamma \left(1+{\frac {1}{k}},-\ln(1-\alpha )\right),} where Γ ( s , x ) {\displaystyle \Gamma (s,x)} is the upper incomplete gamma function. If the

    Tail value at risk

    Tail_value_at_risk

  • Caputo fractional derivative
  • Generalization in fractional calculus

    }}}\,\operatorname {d} t} where Γ ( ⋅ ) {\textstyle \Gamma \left(\cdot \right)} is the Gamma function. Let's define D x α := d α d ⁡ x α {\textstyle \operatorname

    Caputo fractional derivative

    Caputo_fractional_derivative

  • Erlang distribution
  • Family of continuous probability distributions

    {\gamma (k,\lambda x)}{\Gamma (k)}}={\frac {\gamma (k,\lambda x)}{(k-1)!}},} where γ {\displaystyle \gamma } is the lower incomplete gamma function and

    Erlang distribution

    Erlang distribution

    Erlang_distribution

  • Riemann zeta function
  • Analytic function in mathematics

    {d} x} is the gamma function. The Riemann zeta function is defined for other complex values via analytic continuation of the function defined for σ >

    Riemann zeta function

    Riemann zeta function

    Riemann_zeta_function

  • Nakagami distribution
  • Statistical distribution

    }}x^{2}\right)}{\Gamma (m)}}=P\left(m,{\frac {m}{\Omega }}x^{2}\right)} where P is the regularized (lower) incomplete gamma function. The parameters m

    Nakagami distribution

    Nakagami distribution

    Nakagami_distribution

  • Hypergeometric function
  • Function defined by a hypergeometric series

    non-negative integer, one has 2F1(z) → ∞. Dividing by the value Γ(c) of the gamma function, we have the limit: lim c → − m 2 F 1 ( a , b ; c ; z ) Γ ( c ) = (

    Hypergeometric function

    Hypergeometric function

    Hypergeometric_function

  • Nonelementary integral
  • Integrals not expressible in closed-form from elementary functions

    logarithmic integral) x c − 1 e − x {\displaystyle {x^{c-1}}e^{-x}} (incomplete gamma function); for c = 0 , {\displaystyle c=0,} the antiderivative can be written

    Nonelementary integral

    Nonelementary_integral

  • Keith Geddes
  • Canadian mathematician (born 1947)

    Maple Risch algorithm Symbolic integration Derivatives of the incomplete gamma function List of University of Waterloo people Keith Geddes' home page

    Keith Geddes

    Keith_Geddes

  • Gompertz distribution
  • Continuous probability distribution, named after Benjamin Gompertz

    exponential integral and Γ ( ⋅ , ⋅ ) {\displaystyle \Gamma (\cdot ,\cdot )} is the upper incomplete gamma function. If X is defined to be the result of sampling

    Gompertz distribution

    Gompertz distribution

    Gompertz_distribution

  • Harmonic number
  • Sum of the first n whole number reciprocals; 1/1 + 1/2 + 1/3 + ... + 1/n

    {Ein} (z)=\mathrm {E} _{1}(z)+\gamma +\ln z=\Gamma (0,z)+\gamma +\ln z} where Γ(0, z) is the incomplete gamma function. The harmonic numbers have several

    Harmonic number

    Harmonic number

    Harmonic_number

  • Lerch transcendent
  • Special mathematical function

    |a|<1;\Re (s)<0;z\notin (0,\infty ).} An asymptotic series in the incomplete gamma function Φ ( z , s , a ) = 1 2 a s + 1 z a ∑ k = 1 ∞ e − 2 π i ( k − 1

    Lerch transcendent

    Lerch_transcendent

  • Lists of integrals
  • Rules for computing derivatives of functions Incomplete gamma function – Types of special mathematical functions Indefinite sum – Inverse of a finite

    Lists of integrals

    Lists_of_integrals

  • Laguerre polynomials
  • Sequence of differential equation solutions

    }}\Re (\gamma )>-{\tfrac {1}{2}}} for the exponential function. The incomplete gamma function has the representation Γ ( α , x ) = x α e − x ∑ i = 0

    Laguerre polynomials

    Laguerre polynomials

    Laguerre_polynomials

  • Computer algebra system
  • Mathematical software

    radicals) Derivatives of elementary functions and special functions. (e.g. See derivatives of the incomplete gamma function.) Cylindrical algebraic decomposition

    Computer algebra system

    Computer_algebra_system

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

    Borwein & Borwein. The elementary functions are constructed by composing arithmetic operations, the exponential function ( exp {\displaystyle \exp } ), the

    Computational complexity of mathematical operations

    Computational complexity of mathematical operations

    Computational_complexity_of_mathematical_operations

  • Sérsic profile
  • Mathematical function

    {\displaystyle \gamma } are respectively the Gamma function and lower incomplete Gamma function. Many related expressions, in terms of the surface brightness

    Sérsic profile

    Sérsic profile

    Sérsic_profile

  • Integral
  • Operation in mathematical calculus

    antiderivatives, the special functions (like the Legendre functions, the hypergeometric function, the gamma function, the incomplete gamma function and so on). Extending

    Integral

    Integral

    Integral

  • Meijer G-function
  • Generalization of the hypergeometric function

    terms of the Meijer G-function. Here, γ and Γ are the lower and upper incomplete gamma functions, Jν and Yν are the Bessel functions of the first and second

    Meijer G-function

    Meijer G-function

    Meijer_G-function

  • Transport integrals
  • {\frac {e^{t}}{(e^{t}-1)^{2}}}=\sum _{k=0}^{\infty }k\,e^{kt}.} Incomplete gamma function Rogers, William; Powell, Robert (July 3, 1958). Tables of transport

    Transport integrals

    Transport_integrals

  • Gompertz–Makeham law of mortality
  • Mathematical equation related to human death rate

    integral has a closed form in terms of the upper incomplete gamma function Γ ( s , z ) {\displaystyle \Gamma (s,z)} . One convenient expression is E ⁡ [ X

    Gompertz–Makeham law of mortality

    Gompertz–Makeham law of mortality

    Gompertz–Makeham_law_of_mortality

  • Debye function
  • Mathematical function

    0}D_{n}(x)=1.} If Γ {\displaystyle \Gamma } is the gamma function and ζ {\displaystyle \zeta } is the Riemann zeta function, then, for x ≫ 0 {\displaystyle

    Debye function

    Debye_function

  • Mahler polynomial
  • Mahler in his work on the zeros of the incomplete gamma function. Mahler polynomials are given by the generating function ∑ g n ( x ) t n / n ! = exp ⁡ ( x

    Mahler polynomial

    Mahler_polynomial

  • Noncentral chi-squared distribution
  • Noncentral generalization of the chi-squared distribution

    {\gamma (k/2,x/2)}{\Gamma (k/2)}}\,} and where γ ( k , z ) {\displaystyle \gamma (k,z)\,} is the lower incomplete gamma function. The Marcum Q-function

    Noncentral chi-squared distribution

    Noncentral chi-squared distribution

    Noncentral_chi-squared_distribution

  • Jacobi elliptic functions
  • Mathematical function

    \theta } be the incomplete elliptic integral of the second kind with parameter m {\displaystyle m} . Then the Jacobi epsilon function can be defined as

    Jacobi elliptic functions

    Jacobi_elliptic_functions

  • Sine and cosine
  • Fundamental trigonometric functions

    the functional equation for the Gamma function, Γ ( s ) Γ ( 1 − s ) = π sin ⁡ ( π s ) , {\displaystyle \Gamma (s)\Gamma (1-s)={\pi \over \sin(\pi s)},}

    Sine and cosine

    Sine and cosine

    Sine_and_cosine

  • Symbolic integration
  • Computation of an antiderivatives

    pattern-matching and the exploitation of special functions, in particular the incomplete gamma function. Although this approach is heuristic rather than

    Symbolic integration

    Symbolic_integration

  • Bessel function
  • Family of solutions to related differential equations

    _{m=0}^{\infty }{\frac {(-1)^{m}}{m!\,\Gamma (m+\alpha +1)}}{\left({\frac {x}{2}}\right)}^{2m+\alpha },} where Γ(z) is the gamma function, a shifted generalization

    Bessel function

    Bessel function

    Bessel_function

  • Risch algorithm
  • Method for evaluating indefinite integrals

    portal Axiom (computer algebra system) Closed-form expression Incomplete gamma function Lists of integrals Liouville's theorem (differential algebra)

    Risch algorithm

    Risch_algorithm

  • Borel summation
  • Summation method for divergent series

    dt={\frac {1}{z}}\cdot e^{1/z}\cdot \Gamma \left(0,{\frac {1}{z}}\right)} (where Γ is the incomplete gamma function). This integral converges for all z ≥ 0

    Borel summation

    Borel_summation

  • Arrhenius equation
  • Formula for temperature dependence of rates of chemical reactions

    E_{\mathrm {a} }} ⁠ as lower bound and so are often of the type of incomplete gamma functions, which turn out to be proportional to ⁠ exp ⁡ − E a R T {\displaystyle

    Arrhenius equation

    Arrhenius_equation

  • Modified half-normal distribution
  • Probability distribution

    \gamma (s,y)=\int _{0}^{y}t^{s-1}e^{-t}\,dt} denotes the lower incomplete gamma function. The modified half-normal distribution is an exponential family

    Modified half-normal distribution

    Modified_half-normal_distribution

  • Displaced Poisson distribution
  • λ ) {\displaystyle I\left(r,\lambda \right)} is the Pearson's incomplete gamma function: I ( r , λ ) = ∑ y = r ∞ e − λ λ y y ! , {\displaystyle I(r,\lambda

    Displaced Poisson distribution

    Displaced Poisson distribution

    Displaced_Poisson_distribution

  • Home advantage
  • Advantage a team has playing in home venue

    k_{-1}+1)} , where I 1 / 2 ( ) {\displaystyle I_{1/2}()} is incomplete gamma function. For example, Newcastle in 2015/2016 English Premier League season

    Home advantage

    Home_advantage

  • Sinc function
  • Special mathematical function defined as sin(x)/x

    }\left(1-{\frac {x^{2}}{n^{2}}}\right)} and is related to the gamma function Γ(x), as well as to Gauss' Pi function, through Euler's reflection formula: sin ⁡ ( π x

    Sinc function

    Sinc function

    Sinc_function

  • Engel expansion
  • Sum of pairwise divisible unit fractions

    +2\beta ),\dots \}\;} , where γ {\displaystyle \gamma } represents the lower Incomplete gamma function. Specifically, if α = β {\displaystyle \alpha =\beta

    Engel expansion

    Engel_expansion

  • SRGB
  • Standard RGB color space

    denoted with the letter γ {\displaystyle \gamma } , hence the common name "gamma correction" for this function. This design has the benefit of displaying

    SRGB

    SRGB

    SRGB

  • Circular law
  • On eigenvalues of random matrices

    \Gamma (j;x)=\int _{x}^{\infty }t^{j-1}e^{-t}dt} denotes the upper incomplete gamma function. It has the following asymptotics K ∞ b ( w , z ) := lim N → ∞

    Circular law

    Circular_law

  • Combustion
  • Chemical reaction between a fuel and oxygen

    {C_{\mathit {\alpha }}H_{\mathit {\beta }}O_{\mathit {\gamma }}}}+\left(\alpha +{\frac {\beta }{4}}-{\frac {\gamma }{2}}\right)\left({\ce {O_{2}}}+3.77{\ce

    Combustion

    Combustion

    Combustion

  • Spiral
  • Curve that winds around a central point

    Analytic parametric equations of log-aesthetic curves in terms of incomplete gamma functions. Computer Aided Geometric Design 29 (2), 129—140 [7]. Ziatdinov

    Spiral

    Spiral

    Spiral

  • Beta prime distribution
  • Probability distribution

    {x}{1+x}}\left(\alpha ,\beta \right),} where I is the regularized incomplete beta function. While the related beta distribution is the conjugate prior distribution

    Beta prime distribution

    Beta prime distribution

    Beta_prime_distribution

  • Beta distribution
  • Probability distribution

    -1}\end{aligned}}} where Γ ( z ) {\displaystyle \Gamma (z)} is the gamma function. The beta function, B {\displaystyle \mathrm {B} } , is a normalization

    Beta distribution

    Beta distribution

    Beta_distribution

  • Aquifer test
  • Pumping water into an aquifer to monitor its response

    "Well function" (called the incomplete gamma function, Γ ( 0 , u ) {\displaystyle \Gamma (0,u)} , in non-hydrogeology literature). The well function is given

    Aquifer test

    Aquifer_test

  • Generating function transformation
  • Operation on formal power series

    closed-form exponential generating function expanded in terms of the natural logarithm, the incomplete gamma function, and the exponential integral given

    Generating function transformation

    Generating_function_transformation

  • Student's t-distribution
  • Probability distribution

    is the number of degrees of freedom, and Γ {\displaystyle \Gamma } is the gamma function. This may also be written as f ( t ) = 1 ν B ( 1 2 , ν 2 ) (

    Student's t-distribution

    Student's t-distribution

    Student's_t-distribution

  • Complete Fermi–Dirac integral
  • Mathematical integral

    where η {\displaystyle \eta } is the Dirichlet eta function. Incomplete Fermi–Dirac integral Gamma function Polylogarithm Gradshteyn, Izrail Solomonovich;

    Complete Fermi–Dirac integral

    Complete_Fermi–Dirac_integral

  • ARGUS distribution
  • Probability distribution in physics

    \qquad c>0,\,\chi >0,\,p>-1} where Γ(·) is the gamma function, and Γ(·,·) is the upper incomplete gamma function. Here parameters c, χ, p represent the cutoff

    ARGUS distribution

    ARGUS distribution

    ARGUS_distribution

  • List of indefinite sums
  • _{x}\Gamma (x)=(-1)^{x+1}\Gamma (x){\frac {\Gamma (1-x,-1)}{e}}+C} [citation needed] where Γ ( s , x ) {\displaystyle \Gamma (s,x)} is the incomplete gamma

    List of indefinite sums

    List_of_indefinite_sums

  • Harmonic Maass form
  • Mathematical function

    s − 1 e − t d t {\displaystyle \Gamma (s,y)=\int _{y}^{\infty }t^{s-1}e^{-t}dt} denotes the incomplete gamma function (which has to be interpreted appropriately

    Harmonic Maass form

    Harmonic_Maass_form

  • Gauss's continued fraction
  • Mathematical concept

    expansions for the Fresnel integrals, for the Dawson function, and for the incomplete gamma function. A simpler version of the argument yields two useful

    Gauss's continued fraction

    Gauss's_continued_fraction

  • Likelihood function
  • Function related to statistics and probability theory

    derivatives of the sufficient statistic T and the log-partition function A. The gamma distribution is an exponential family with two parameters, α {\textstyle

    Likelihood function

    Likelihood_function

  • Completeness (logic)
  • Characteristic of some logical systems

    system, i.e. is one of its theorems; otherwise the system is said to be incomplete. The term "complete" is also used without qualification, with differing

    Completeness (logic)

    Completeness_(logic)

  • Scaled inverse chi-squared distribution
  • Probability distribution

    , x ) {\displaystyle \Gamma (a,x)} is the incomplete gamma function, Γ ( x ) {\displaystyle \Gamma (x)} is the gamma function and Q ( a , x ) {\displaystyle

    Scaled inverse chi-squared distribution

    Scaled inverse chi-squared distribution

    Scaled_inverse_chi-squared_distribution

  • Moment generating function
  • Concept in probability theory and statistics

    theory and statistics, the moment generating function of a real-valued random variable is a generating function that provides an alternative specification

    Moment generating function

    Moment_generating_function

  • Order of integration (calculus)
  • Order in which multiple or iterated integrals are computed

    ISBN 0-521-38991-7. M. Aslam Chaudhry & Syed M. Zubair (2001). On a Class of Incomplete Gamma Functions with Applications. CRC Press. p. Appendix C. ISBN 1-58488-143-7

    Order of integration (calculus)

    Order_of_integration_(calculus)

  • Twisting properties
  • ) {\displaystyle \Gamma (a,b)} the incomplete gamma function and F R k ( r K ) {\displaystyle F_{R_{k}}(r_{K})} the Fox's H function that can be approximated

    Twisting properties

    Twisting_properties

  • Negative binomial distribution
  • Probability distribution

    {(k+r-1)(k+r-2)\dotsm (r)}{k!}}={\frac {\Gamma (k+r)}{k!\ \Gamma (r)}}=\left(\!\!{r \choose k}\!\!\right).} Note that Γ(r) is the Gamma function, and ( ( r k ) ) {\displaystyle

    Negative binomial distribution

    Negative binomial distribution

    Negative_binomial_distribution

  • Loss functions for classification
  • Concept in machine learning

    =f^{-1}(\gamma F(x))} . In conclusion, by choosing a loss function with larger margin (smaller γ {\displaystyle \gamma } ) we increase regularization and improve our

    Loss functions for classification

    Loss functions for classification

    Loss_functions_for_classification

  • F-distribution
  • Continuous probability distribution

    I x ( a , b ) {\displaystyle I_{x}(a,b)} ⁠ is the regularized incomplete beta function. The expectation, variance, and other details about the F-distribution

    F-distribution

    F-distribution

    F-distribution

  • Feynman diagram
  • Pictorial representation of the behavior of subatomic particles

    sometimes incomplete. The uncancelled denominator is called the symmetry factor of the diagram. The contribution of each diagram to the correlation function must

    Feynman diagram

    Feynman diagram

    Feynman_diagram

  • Noncentral t-distribution
  • Probability distribution

    the gamma function and I is the regularized incomplete beta function. Although there are other forms of the cumulative distribution function, the first

    Noncentral t-distribution

    Noncentral t-distribution

    Noncentral_t-distribution

  • Yule–Simon distribution
  • Discrete probability distribution

    f(k;\rho )={\frac {\rho \Gamma (\rho +1)}{(k+\rho )^{\underline {\rho +1}}}},} where Γ {\displaystyle \Gamma } is the gamma function. Thus, if ρ {\displaystyle

    Yule–Simon distribution

    Yule–Simon distribution

    Yule–Simon_distribution

  • Lauricella hypergeometric series
  • Well defined hypergeometric series discovered by Giuseppe Lauricella

    The representation implies that the incomplete elliptic integral Π is a special case of Lauricella's function FD with three variables: Π ( n , ϕ , k

    Lauricella hypergeometric series

    Lauricella_hypergeometric_series

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Online names & meanings

  • Junaid
  • Girl/Female

    Arabic

    Junaid

    Fighter; Equal to Small Army

  • Viera
  • Girl/Female

    Australian, Czech, Jamaican

    Viera

    Latin True; Russian Faith

  • Heema
  • Girl/Female

    Indian

    Heema

    Gold, Snow

  • Rajath | ரஜத
  • Boy/Male

    Tamil

    Rajath | ரஜத

    Silver or courage

  • Shifu
  • Girl/Female

    Indian

    Shifu

    Teacher

  • Filma
  • Girl/Female

    Anglo, British, English

    Filma

    Veiled

  • STEFFIE
  • Female

    English

    STEFFIE

    Pet form of English Stefanie, STEFFIE means "crown."

  • Tejasa
  • Boy/Male

    Hindu, Indian, Sanskrit

    Tejasa

    Radiant Energy; Majesty

  • Muneera
  • Girl/Female

    Indian

    Muneera

    Illuminating, Shedding light, Bright and shining

  • Ashoka
  • Girl/Female

    Indian

    Ashoka

    No sorrow, Without worries, Without grief

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INCOMPLETE GAMMA-FUNCTION

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INCOMPLETE GAMMA-FUNCTION

  • Uncomplete
  • a.

    Incomplete.

  • Gummous
  • a.

    Of or pertaining to a gumma.

  • Incomplete
  • a.

    Wanting any of the usual floral organs; -- said of a flower.

  • Gummatous
  • a.

    Belonging to, or resembling, gumma.

  • Assonance
  • n.

    Incomplete correspondence.

  • Yamma
  • n.

    The llama.

  • Incomplete
  • a.

    Not complete; not filled up; not finished; not having all its parts, or not having them all adjusted; imperfect; defective.

  • Gamba
  • n.

    A viola da gamba.

  • Complete
  • a.

    Finished; ended; concluded; completed; as, the edifice is complete.

  • Mammy
  • n.

    A child's name for mamma, mother.

  • Mama
  • n.

    See Mamma.

  • Mam
  • n.

    Mamma.

  • Incompletely
  • adv.

    In an incomplete manner.

  • Mamma
  • n.

    A glandular organ for secreting milk, characteristic of all mammals, but usually rudimentary in the male; a mammary gland; a breast; under; bag.

  • Complete
  • v. t.

    To bring to a state in which there is no deficiency; to perfect; to consummate; to accomplish; to fulfill; to finish; as, to complete a task, or a poem; to complete a course of education.

  • Gamma
  • n.

    The third letter (/, / = Eng. G) of the Greek alphabet.

  • Gemmae
  • pl.

    of Gemma

  • Mammae
  • pl.

    of Mamma

  • Baritone
  • n.

    The viola di gamba, now entirely disused.

  • Gummata
  • pl.

    of Gumma