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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
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
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
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)
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
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
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
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
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
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
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
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
Statistical function that defines the quantiles of a probability distribution
probability distribution's quantile function is the inverse of its cumulative distribution function. That is, the quantile function of a distribution D {\displaystyle
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
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 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
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
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 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
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 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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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
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
Hyperbolic analogues of trigonometric functions
A=(e^{-u},e^{u}),\ B=(e^{u},\ e^{-u}),\ OA+OB=OC} . Hyperbolic sine: the odd part of the exponential function, that is, sinh x = e x − e − x 2 = e 2
Hyperbolic_functions
Class of mathematical function
of complex analysis, a meromorphic function on an open subset D {\displaystyle D} of the complex plane is a function that is holomorphic on all of D {\displaystyle
Meromorphic_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
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 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
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
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
Generalized function whose value is zero everywhere except at zero
Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_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
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 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
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
Mathematical function that can be computed by a program
Computable functions are the basic objects of study in computability theory. Informally, a function is computable if there is an algorithm that computes
Computable_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
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
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
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
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
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
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
In mathematics, the Toronto function T(m,n,r) is a modification of the confluent hypergeometric function defined by Heatley (1943), Weisstein, as T ( m
Toronto_function
The Export function is an idea used in economic theories to measure exports. The total amount of exports, E, in a nation is mainly affected by two variables
Export_function
In mathematics, the crenel function is a periodic discontinuous function P(x) defined as 1 for x belonging to a given interval and 0 outside of it. It
Crenel_function
applied mathematics, the Kelvin functions berν(x) and beiν(x) are the real and imaginary parts, respectively, of J ν ( x e 3 π i 4 ) , {\displaystyle J_{\nu
Kelvin_functions
Mathematical function with no sudden changes
a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies
Continuous_function
Generalization of the Jack polynomial
In mathematics, the Jack function is a generalization of the Jack polynomial, introduced by Henry Jack. The Jack polynomial is a homogeneous, symmetric
Jack_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
In number theory, the unit function is a completely multiplicative function on the positive integers defined as: ε ( n ) = { 1 , if n = 1 0 , if n ≠
Unit_function
Function that applies a set to itself
transformation, transform, or self-map is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X. Examples include linear
Transformation_(function)
Model for genetics of flower development
sexually mature state (i.e. a transition towards flowering); secondly, the transformation of the apical meristem's function from a vegetative meristem
ABC model of flower development
ABC_model_of_flower_development
Function in statistics
inverse of the standard logistic function σ ( x ) = 1 / ( 1 + e − x ) {\displaystyle \textstyle \sigma (x)=1/(1+e^{-x})} , so the logit is defined
Logit
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
E FUNCTION
E FUNCTION
Female
French
Feminine form of French Iréné, IRÉNÉE means "peaceful."
Female
French
Feminine form of French unisex Esmé, ESMÉE means "esteemed, loved."
Female
French
Feminine form of French André, ANDRÉE means "man; warrior."
Female
French
Feminine form of French Honoré, HONORÉE means "honor, valor."
Boy/Male
English, Modern
A Miracle; Inimitably; Do Something which Others cannot do
Girl/Female
French, German, Latin
Virgin
Female
French
French form of Latin Medea, MÉDÉE means "cunning."
Male
Slovene
Pet form of Slovene Jožef, JOŽE means "(God) shall add (another son)."Â
Boy/Male
American, British, English
Birch
Female
French
French name, derived from the French word aimée, AIMÉE means "much loved."
Female
French
French form of Latin Dorothea, DOROTHÉE means "gift of God."
Female
French
Feminine form of French Désiré, DÉSIRÉE means "desired."Â
Female
French
Pet form of French Estelle, ESTÉE means "star."
Female
French
Feminine form of French Dieudonné, DIEUDONNÉE means "God-given."
Male
French
French form of Latin Timotheus, TIMOTHÉE means "to honor God."
Girl/Female
French, German, Latin, Spanish
Modest
Female
French
Feminine form of French René, RENÉE means "reborn."
Female
French
French feminine form of Latin Josephus, JOSÉE means "(God) shall add (another son)."Â
Boy/Male
American, British, English
Bird
Male
French
French form of Latin Isaias, ISAÃE means "God is salvation."
E FUNCTION
E FUNCTION
Girl/Female
Greek
Peace.
Boy/Male
Tamil
Lord of the world
Boy/Male
Shakespearean
Cymbeline' King of Britain.
Girl/Female
Muslim/Islamic
Light
Boy/Male
Tamil
Girl/Female
American, Australian, British, Christian, English, French, Greek, Hebrew, Italian
Butterfly; Diminutive of Vanessa; The Mystic Goddess of an Ancient Greek Brotherhood; God is Gracious; Merciful
Boy/Male
German, Hindu, Indian
Brave
Boy/Male
Russian
Little.
Girl/Female
Biblical
Tower compassed about.
Boy/Male
Hindu, Indian, Telugu
Name of a River
E FUNCTION
E FUNCTION
E FUNCTION
E FUNCTION
E FUNCTION
n.
Originally, the highest note in the scale of Guido; hence, proverbially, any extravagant saying.
n.
See Set, n., 2 (e) and 3.
n.
See Elevator, n. (e).
n.
An evergreen shrub of the genus Erica (E. passerina).
a.
Bold; brave; stout; daring; resolu?e; intrepid.
e
(imp.) of Wit
a.
Covered with a mant/e; cloaked; disguised.
n.
A female pope; i. e., the fictitious pope Joan.
e. i.
To cut with a grating sound; to cut; to penetrate or pierce harshly; as, the griding sword.
a.
Lower by a semitone; flat; as, E molle, that is, E flat.
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.
v. t.
To liken; to compa/e.
pl.
of Notopodium
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.
e. t.
To make cool.
a.
Old; as, Auld Reekie (old smoky), i. e., Edinburgh.