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In mathematics, E-functions are a type of power series that satisfy particular arithmetic conditions on the coefficients. They are of interest in transcendental
E-function
Extension of the factorial function
( x ) {\displaystyle \ln(x)} or log e ( x ) {\displaystyle \log _{e}(x)} . In mathematics, the gamma function (represented by Γ {\displaystyle \Gamma
Gamma_function
Mathematical function, denoted exp(x) or e^x
function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. It is denoted e x {\displaystyle e^{x}}
Exponential_function
S-shaped curve
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation f ( x ) = L 1 + e − k ( x − x 0 ) {\displaystyle f(x)={\frac
Logistic_function
Topics referred to by the same term
Look up function or functionality in Wiktionary, the free dictionary. Function or functionality may refer to: Function key, a type of key on computer keyboards
Function
Sigmoid shape special function
error function (also called the Gauss error function), often denoted by e r f {\displaystyle \mathbf {erf} } , is the function erf ( z ) = 2 π ∫ 0 z e −
Error_function
Association of one output to each input
mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the
Function_(mathematics)
In mathematics, the E-function was introduced by Thomas Murray MacRobert (1937–1938) to extend the generalized hypergeometric series pFq(·) to the case
MacRobert_E_function
Multivalued function in mathematics
relation of the function f ( w ) = w e w {\displaystyle f(w)=we^{w}} , where w {\displaystyle w} is any complex number and e w {\displaystyle e^{w}} is the
Lambert_W_function
Family of solutions to related differential equations
Bessel functions are a class of special functions that commonly appear in problems involving wave motion, heat conduction, and other physical phenomena
Bessel_function
Program function without side effects
variables, mutable reference arguments or input streams, i.e., referential transparency), and the function has no side effects (no mutation of non-local variables
Pure_function
Polynomial function of degree 4
algebra, a quartic function is a function of the form f ( x ) = a x 4 + b x 3 + c x 2 + d x + e , {\displaystyle f(x)=ax^{4}+bx^{3}+cx^{2}+dx+e,} where a is
Quartic_function
Nutrients required by organisms in small amounts
are essential to an organism in small quantities for proper metabolic function. These essential nutrients cannot be synthesized in the organism in sufficient
Vitamin
Statistical function that defines the quantiles of a probability distribution
the quantile function of a probability distribution is the inverse of its cumulative distribution function. That is, the quantile function of a distribution
Quantile_function
Generalization of the hypergeometric function
kind: the generalized hypergeometric function and the MacRobert E-function had the same aim, but Meijer's G-function was able to include those as particular
Meijer_G-function
Real function with secant line between points above the graph itself
function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph of the function
Convex_function
Complex complementary error function
Faddeeva function or Kramp function is a scaled complex complementary error function, w ( z ) := e − z 2 erfc ( − i z ) = erfcx ( − i z ) = e − z 2 (
Faddeeva_function
Logarithm to the base of the mathematical constant e
the inverse function of the exponential function e x {\displaystyle e^{x}} , so that e ln ( x ) = x {\displaystyle e^{\ln(x)}=x} or ln ( e x ) = x {\displaystyle
Natural_logarithm
Mathematical function having a characteristic S-shaped curve or sigmoid curve
sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the
Sigmoid_function
Family of power series in mathematics
coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over
Generalized hypergeometric function
Generalized_hypergeometric_function
Complex exponential in terms of sine and cosine
between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has e i x = cos x + i sin
Euler's_formula
Mathematical activation function in data analysis
The swish function is a family of mathematical function defined as follows: swish β ( x ) = x sigmoid ( β x ) = x 1 + e − β x . {\displaystyle \operatorname
Swish_function
Functions in mathematics
the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R {\displaystyle f:U\to \mathbb {R} }
Harmonic_function
Order-preserving mathematical function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept
Monotonic_function
Function that is continuous everywhere but differentiable nowhere
mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere
Weierstrass_function
Polynomial function of degree 5
In mathematics, a quintic function is a function of the form g ( x ) = a x 5 + b x 4 + c x 3 + d x 2 + e x + f , {\displaystyle g(x)=ax^{5}+bx^{4}+cx^{3}+dx^{2}+ex+f
Quintic_function
Functions of an angle
mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of
Trigonometric_functions
Analytic function in mathematics
The Riemann zeta function or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ (zeta), is a mathematical function of a complex variable
Riemann_zeta_function
It can be defined in terms of the confluent hypergeometric function U, by ω m , n ( x ) = e − x + π i ( m / 2 − n ) Γ ( 1 + n − m / 2 ) U ( m / 2 − n
Cunningham_function
Operation on mathematical functions
two functions, f {\displaystyle f} and g {\displaystyle g} , and returns a new function f ∘ g {\displaystyle f\circ g} . When the composite function f ∘
Function_composition
Mathematical function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f ( x ) = exp ( − x 2 ) {\displaystyle f(x)=\exp(-x^{2})}
Gaussian_function
Type of function in mathematics
an analytic function is a function that is locally represented by a convergent power series. More precisely, a real or complex function is analytic at
Analytic_function
Special mathematical function defined as sin(x)/x
In mathematics, physics and engineering, the sinc function (/ˈsɪŋk/ SINK), denoted by sinc(x), is defined as either sinc ( x ) = sin x x . {\displaystyle
Sinc_function
Smooth and compactly supported function
analysis, a bump function is a localized auxiliary function, usually chosen to be smooth and to have compact support. Bump functions are commonly used
Bump_function
Function with a repeating pattern
A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which are used to describe waves
Periodic_function
Mathematical function whose derivative exists
or complex function of a single variable is differentiable if its derivative exists at each point in its domain. For real-valued functions of a real variable
Differentiable_function
Mapping arbitrary data to fixed-size values
A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support
Hash_function
Function whose domain is the positive integers
log e ( x ) {\displaystyle \log _{e}(x)} . In number theory, an arithmetic, arithmetical, or number-theoretic function is generally any function whose
Arithmetic_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
Mathematical function
In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: ψ ( z ) = d d z ln Γ ( z ) = Γ ′ ( z ) Γ ( z )
Digamma_function
Mathematical relation assigning a probability event to a cost
optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one
Loss_function
Function in probability theory
function C(x, y) gives the covariance of the values of the random field at the two locations x and y: C ( x , y ) := cov ( Z ( x ) , Z ( y ) ) = E [
Covariance_function
2.71828...; base of natural logarithms
The number e is a mathematical constant, approximately equal to 2.71828, that is the base of the natural logarithm and exponential function. It is sometimes
E_(mathematical_constant)
Mathematical function
the Riemann–Siegel Z function, the Riemann–Siegel zeta function, the Hardy function, the Hardy Z function and the Hardy zeta function. It can be defined
Z_function
Mathematical description of quantum state
In quantum mechanics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common
Wave_function
Smoothed ramp function
softplus function is f ( x ) = ln ( 1 + e x ) . {\displaystyle f(x)=\ln(1+e^{x}).} It is a smooth approximation (in fact, an analytic function) to the
Softplus
Polynomial function of degree two
In mathematics, a quadratic function of a single variable is a function of the form f ( x ) = a x 2 + b x + c {\displaystyle f(x)=ax^{2}+bx+c} with
Quadratic_function
Multiplicative function in number theory
The Möbius function μ ( n ) {\displaystyle \mu (n)} is a multiplicative function in number theory introduced by the German mathematician August Ferdinand
Möbius_function
In vector calculus, an invex function is a differentiable function f {\displaystyle f} from R n {\displaystyle \mathbb {R} ^{n}} to R {\displaystyle \mathbb
Invex_function
Mathematical function such that every output has at least one input
surjective function (also known as surjection, or onto function /ˈɒn.tuː/) is a function f such that, for every element y of the function's codomain, there
Surjective_function
Mathematical function
or log e ( x ) {\displaystyle \log _{e}(x)} . In mathematics, the Chebyshev function is either a scalarising function (Tchebycheff function) or one
Chebyshev_function
In mathematics, the Bateman function (or k-function) is a special case of the confluent hypergeometric function studied by Harry Bateman(1931). Bateman
Bateman_function
Mathematical function
one-parameter Mittag-Leffler function, introduced by Gösta Mittag-Leffler in 1903, can be defined by the Maclaurin series E α ( z ) = ∑ k = 0 ∞ z k Γ (
Mittag-Leffler_function
Smooth approximation of one-hot arg max
The softmax function, also known as softargmax or normalized exponential function, converts a tuple of K real numbers into a probability distribution
Softmax_function
Summatory function of the Möbius function
In number theory, the Mertens function is defined for all positive integers n as M ( n ) = ∑ k = 1 n μ ( k ) , {\displaystyle M(n)=\sum _{k=1}^{n}\mu (k)
Mertens_function
Function with variable number of arguments
variadic function is a function of indefinite arity, i.e., one which accepts a variable number of arguments. Support for variadic functions differs widely
Variadic_function
Mathematical concept
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists
Inverse_function
Polynomial function of degree 3
In mathematics, a cubic function is a function of the form f ( x ) = a x 3 + b x 2 + c x + d , {\displaystyle f(x)=ax^{3}+bx^{2}+cx+d,} with a ≠ 0 {\displaystyle
Cubic_function
Function specifying the behavior of a component in an electronic or control system
a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models
Transfer_function
Method of solution to differential equations
In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with
Green's_function
Quickly growing function
Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not
Ackermann_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 the
Theta_function
Integral of the Gaussian function, equal to sqrt(π)
Euler–Poisson integral, is the integral of the Gaussian function f ( x ) = e − x 2 {\displaystyle f(x)=e^{-x^{2}}} over the entire real line. Named after the
Gaussian_integral
Function that preserves distinctness
In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct
Injective_function
Function representing the number of primes less than or equal to a given number
{\displaystyle \ln(x)} or log e ( x ) {\displaystyle \log _{e}(x)} . In mathematics, the prime-counting function is the function counting the number of prime
Prime-counting_function
Artificial neural network node function
In artificial neural networks, the activation function of a node is a function that calculates the output of the node based on its individual inputs and
Activation_function
Fast summation method in mathematics
In mathematics, the FEE method, or fast E-function evaluation method, is the method of fast summation of series of a special form. It was constructed in
FEE_method
Function that returns its argument unchanged
mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the value
Identity_function
Function defined by a hypergeometric series
hypergeometric function 2F1(a, b; c; z) is a special function represented by the hypergeometric series, that includes many other special functions as specific
Hypergeometric_function
Mathematical function characterizing set membership
In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all
Indicator_function
Class of mathematical functions
Intuitively, subharmonic functions are related to convex functions of one variable as follows. If the graph of a convex function and a line intersect at
Subharmonic_function
Type of mathematical function
elementary function is a function of a single variable (real or complex) that is typically encountered by beginners. The basic elementary functions are polynomial
Elementary_function
Function defined by multiple sub-functions
mathematics, a piecewise function (also called a piecewise-defined function, a hybrid function, or a function defined by cases) is a function whose domain is partitioned
Piecewise_function
Function that is discontinuous at rationals and continuous at irrationals
Thomae's function is a real-valued function of a real variable that can be defined as: f ( x ) = { 1 q if x = p q ( x is rational), with p ∈ Z and
Thomae's_function
Eugene Warren at MIT. The Patterson function is defined as P ( u , v , w ) = ∑ h , k , ℓ ∈ Z | F h , k , ℓ | 2 e − 2 π i ( h u + k v + ℓ w ) . {\displaystyle
Patterson_function
Special function in the physical sciences
mathematics, the Airy function (or Airy function of the first kind) A i ( x ) {\displaystyle \mathbf {Ai({\boldsymbol {x}})} } is a special function named after
Airy_function
Formal power series
generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often
Generating_function
Analytic function that does not satisfy a polynomial equation
mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the independent variable
Transcendental_function
Arithmetic function related to the divisors of an integer
theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number
Divisor_function
Negative of a convex function
In mathematics, a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to
Concave_function
is a utility function u {\displaystyle u} that describes preferences over n goods, the expenditure function e ( p , u ∗ ) {\displaystyle e(p,u^{*})} is
Expenditure_function
Meromorphic function
In mathematics, the polygamma function of order m is a meromorphic function on the complex numbers C {\displaystyle \mathbb {C} } defined as the (m +
Polygamma_function
Function returning minus 1, zero or plus 1
In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether
Sign_function
Point to which functions converge in analysis
mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input which
Limit_of_a_function
Number of integers coprime to and less than n
) {\displaystyle \ln(x)} or log e ( x ) {\displaystyle \log _{e}(x)} . In number theory, Euler's totient function counts the positive integers up to
Euler's_totient_function
Function studied by Ramanujan
Euler function, η {\displaystyle \eta } is the Dedekind eta function, Δ ( z ) {\displaystyle \Delta (z)} is the modular discriminant, and q = e 2 π i
Ramanujan_tau_function
Measurement in petroleum engineering
called TEM-function is a criterion to characterize dynamic two-phase flow characteristics of rocks (or dynamic rock quality). TEM is a function of relative
TEM-function
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
Sexual health concept
Sexual function is how the body reacts in different stages of the sexual response cycle. It is defined as the ability of an individual to react sexually
Sexual_function
Bessel functions. The Weber function (also known as Lommel–Weber function), introduced by H. F. Weber (1879), is a closely related function defined by E ν
Anger_function
Asymmetric sigmoid function
or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes
Gompertz_function
Function returning one of only two values
switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the
Boolean_function
Function related to statistics and probability theory
A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability
Likelihood_function
Mathematical function with convex lower level sets
In mathematics, a quasiconvex function is a real-valued function defined on a convex subset of a real vector space, such that for any real number y, the
Quasiconvex_function
Class of mathematical functions
role in the theory of elliptic functions, i.e., meromorphic functions that are doubly periodic. A ℘-function together with its derivative can be used to
Weierstrass_elliptic_function
Expression in propositional calculus
(e.g. n variables, in which case the function takes n arguments). As a mathematical function, A(x) or A(x1, x2, ..., xn), the propositional function is
Propositional_function
Topics referred to by the same term
In mathematics, omega function refers to a function using the Greek letter omega, written ω or Ω. Ω {\displaystyle \Omega } (big omega) may refer to:
Omega_function
Mathematical function having a characteristic "bell"-shaped curve
A bell-shaped function or simply 'bell curve' is a mathematical function having a characteristic "bell"-shaped curve. These functions are typically continuous
Bell-shaped_function
Complex-differentiable (mathematical) function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood
Holomorphic_function
American health technology company
Function Health, often stylized as simply Function, is an American company and platform headquartered in Austin, Texas. The venture capital-backed company
Function_Health
E FUNCTION
E FUNCTION
Girl/Female
French, German, Latin
Virgin
Female
French
Feminine form of French René, RENÉE means "reborn."
Male
Slovene
Pet form of Slovene Jožef, JOŽE means "(God) shall add (another son)."Â
Boy/Male
American, British, English
Birch
Male
French
French form of Latin Isaias, ISAÃE means "God is salvation."
Female
French
Feminine form of French Désiré, DÉSIRÉE means "desired."Â
Female
French
French name, derived from the French word aimée, AIMÉE means "much loved."
Female
French
Feminine form of French Iréné, IRÉNÉE means "peaceful."
Female
French
Feminine form of French Dieudonné, DIEUDONNÉE means "God-given."
Female
French
French form of Latin Medea, MÉDÉE means "cunning."
Female
French
Feminine form of French Honoré, HONORÉE means "honor, valor."
Female
French
Pet form of French Estelle, ESTÉE means "star."
Female
French
French feminine form of Latin Josephus, JOSÉE means "(God) shall add (another son)."Â
Female
French
Feminine form of French unisex Esmé, ESMÉE means "esteemed, loved."
Male
French
French form of Latin Timotheus, TIMOTHÉE means "to honor God."
Female
French
French form of Latin Dorothea, DOROTHÉE means "gift of God."
Boy/Male
English, Modern
A Miracle; Inimitably; Do Something which Others cannot do
Boy/Male
American, British, English
Bird
Girl/Female
French, German, Latin, Spanish
Modest
Female
French
Feminine form of French André, ANDRÉE means "man; warrior."
E FUNCTION
E FUNCTION
Boy/Male
Australian, Irish, Scandinavian
Excellent; Strength; Vigour
Girl/Female
Dutch American
Sheltering.
Boy/Male
Arabic
Suitable; Proper
Boy/Male
American, British, English, Greek
Victory of the People; Son of Nicholas; Triumphant People; People's Victory
Girl/Female
Arabic, Muslim
Prophet Ibrahim's 4th and Final Wife
Male
Dutch
, mind bright.
Boy/Male
Hindu, Indian
Tool to Project Arrow
Girl/Female
Muslim
Contended
Boy/Male
Anglo Saxon
Bold friend.
Girl/Female
Muslim
Helper. Supporter.
E FUNCTION
E FUNCTION
E FUNCTION
E FUNCTION
E FUNCTION
e
(imp.) of Wit
n.
A female pope; i. e., the fictitious pope Joan.
e. t.
To make cool.
v. t.
To liken; to compa/e.
superl.
Not decidedly marked; not forcible; inconsiderable; unimportant; insignificant; not severe; weak; gentle; -- applied in a great variety of circumstances; as, a slight (i. e., feeble) effort; a slight (i. e., perishable) structure; a slight (i. e., not deep) impression; a slight (i. e., not convincing) argument; a slight (i. e., not thorough) examination; slight (i. e., not severe) pain, and the like.
n.
An evergreen shrub of the genus Erica (E. passerina).
e. i.
To cut with a grating sound; to cut; to penetrate or pierce harshly; as, the griding sword.
superl.
Possessing a characteristic quality in a supreme or superior degree; as, high (i. e., intense) heat; high (i. e., full or quite) noon; high (i. e., rich or spicy) seasoning; high (i. e., complete) pleasure; high (i. e., deep or vivid) color; high (i. e., extensive, thorough) scholarship, etc.
n.
Originally, the highest note in the scale of Guido; hence, proverbially, any extravagant saying.
n.
See Set, n., 2 (e) and 3.
a.
Covered with a mant/e; cloaked; disguised.
a.
Lower by a semitone; flat; as, E molle, that is, E flat.
n.
See Elevator, n. (e).
pl.
of Notopodium
a.
Bold; brave; stout; daring; resolu?e; intrepid.
a.
Old; as, Auld Reekie (old smoky), i. e., Edinburgh.