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Topics referred to by the same term
In mathematics, S-function may refer to: sigmoid function Schur polynomials A function in the Laplace transformed 's-domain' In computer science, It may
S-function
Analytic function in mathematics
{1}{3^{s}}}+\cdots } for R e ( s ) > 1 {\displaystyle \mathrm {Re} (s)>1} , and its analytic continuation elsewhere. The Riemann zeta function plays a
Riemann_zeta_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
Association of one output to each input
non-empty open interval. Such a function is then called a partial function. A function f on a set S means a function from the domain S, without specifying a codomain
Function_(mathematics)
Function with a multiplicative scaling behaviour
function f of n variables is homogeneous of degree k if f ( s x 1 , … , s x n ) = s k f ( x 1 , … , x n ) {\displaystyle f(sx_{1},\ldots ,sx_{n})=s^{k}f(x_{1}
Homogeneous_function
Function in analytic number theory
s ) = ( 1 − 2 1 − s ) ζ ( s ) {\displaystyle \eta (s)=\left(1-2^{1-s}\right)\zeta (s)} Both the Dirichlet eta function and the Riemann zeta function are
Dirichlet_eta_function
Method of solution to differential equations
for the Green's function by f(s), and then integrate with respect to s, we obtain, ∫ L G ( x , s ) f ( s ) d s = ∫ δ ( x − s ) f ( s ) d s = f ( x ) . {\displaystyle
Green's_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
Quickly growing function
(b1)F(S(0),0,n)→S(n)(b2)F(S(0),S(0),0)→S(S(0))(b3)F(S(0),S(S(0)),0)→0(b4)F(S(0),S(S(S(m))),0)→S(0)(b5)F(S(0),S(m),S(n))→F(S(n),m,F(S(0),S(m),0))(b6)F(S(S(x))
Ackermann_function
Extension of the factorial function
zeta function is its functional equation: Γ ( s 2 ) ζ ( s ) π − s 2 = Γ ( 1 − s 2 ) ζ ( 1 − s ) π − 1 − s 2 . {\displaystyle \Gamma \left({\frac {s}{2}}\right)\
Gamma_function
Function specifying the behavior of a component in an electronic or control system
function H ( s ) {\displaystyle H(s)} as Y ( s ) = H ( s ) X ( s ) {\displaystyle Y(s)=H(s)X(s)} and the transfer function itself is H ( s ) = Y ( s )
Transfer_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
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
Integral transform useful in probability theory, physics, and engineering
converts a function of a real variable (usually t {\displaystyle t} , in the time domain) to a function of a complex variable s {\displaystyle s} (in the
Laplace_transform
Elementary operation on a natural number
successor function or successor operation sends a natural number to the next one. The successor function is denoted by S {\displaystyle S} , so S ( n ) =
Successor_function
Special mathematical function
known as Jonquière's function, for Alfred Jonquière) is a special function Lis(z) of order s and argument z. Only for special values of s does the polylogarithm
Polylogarithm
in other contexts complete Bernstein function, Nevanlinna function, Pick function or class (S) function. A function f : I → R {\displaystyle f:I\to \mathbb
Operator_monotone_function
Concept in theoretical computer science
1962 paper, Radó defined two functions related to the busy beaver game: the score function Σ(n) and the shifts function S(n). Both take a number of Turing
Busy_beaver
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
Special function in mathematics
zeta function is one of the many zeta functions. It is formally defined for complex variables s with Re(s) > 1 and a ≠ 0, −1, −2, ... by ζ ( s , a )
Hurwitz_zeta_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
Blood tests indicating the state of the liver
Liver function tests (LFTs or LFs), also referred to as a hepatic panel or liver panel, are groups of blood tests that provide information about the state
Liver_function_tests
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
Meromorphic function on the complex plane
L-function of f {\displaystyle \textstyle f} : Λ ( f , s ) = q ( f ) s / 2 γ ( f , s ) L ( f , s ) . {\displaystyle \Lambda (f,s)=q(f)^{s/2}\gamma (f,s)L(f
L-function
Mathematical function with no sudden changes
continuous function F : X → Y {\displaystyle F\colon X\to Y} such that F ( s ) = f ( s ) {\displaystyle F(s)=f(s)} for every s ∈ S {\displaystyle s\in S} , which
Continuous_function
Indicator function of positive numbers
The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙), is a step function named after Oliver Heaviside
Heaviside_step_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
Types of special mathematical functions
gamma function is defined as γ ( s , x ) = ∫ 0 x t s − 1 e − t d t . {\displaystyle \gamma (s,x)=\int _{0}^{x}t^{s-1}e^{-t}\,dt.} In both cases, s {\displaystyle
Incomplete_gamma_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
Functions in mathematics
the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R {\displaystyle f\colon U\to \mathbb
Harmonic_function
Multiplicative function in number theory
Riemann zeta function; if s {\displaystyle s} is a complex number with real part larger than 1 we have ∑ n = 1 ∞ μ ( n ) n s = 1 ζ ( s ) . {\displaystyle
Möbius_function
Conjecture on zeros of the zeta function
function satisfies the functional equation ζ(s)=2sπs−1 sin(πs2) Γ(1−s) ζ(1−s). One may then define ζ(s) for all remaining nonzero complex numbers s (Re(s)≤0
Riemann_hypothesis
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
Constants of the mathematical zeta function
zeta function is a function in complex analysis, which is also important in number theory. It is often denoted ζ ( s ) {\displaystyle \zeta (s)} and
Particular values of the Riemann zeta function
Particular_values_of_the_Riemann_zeta_function
Index of lists with the same name
zeta function is (usually) a function analogous to the original example, the Riemann zeta function ζ ( s ) = ∑ n = 1 ∞ 1 n s . {\displaystyle \zeta (s)=\sum
List_of_zeta_functions
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
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
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
Category of cloud computing services
Function as a service is a "platform-level cloud capability" that enables its users "to build and manage microservices applications with low initial investment
Function_as_a_service
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 (nowhere-differentiable function)
Weierstrass_function_(nowhere-differentiable_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
Type of mathematical function
mathematics, a Dirichlet L-series is a function of the form L(s,χ)=∑n=1∞χ(n)ns, where χ is a Dirichlet character and s a complex variable with real part greater
Dirichlet_L-function
Conformal mappings in complex analysis
In complex analysis, the Schwarz triangle function or Schwarz s-function is a function that conformally maps the upper half plane to a triangle in the
Schwarz_triangle_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
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
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
Special function defined by an integral
The Fresnel integrals S(x) and C(x), and their auxiliary functions F(x) and G(x) are transcendental functions named after Augustin-Jean Fresnel that are
Fresnel_integral
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
Negative of a convex function
(y,f(y)). A function f is quasiconcave if the upper contour sets of the function S(a)={x:f(x)≥a} are convex sets. A differentiable function f is (strictly)
Concave_function
Program function without side effects
In computer programming, a pure function is a function that has the following properties: the function return values are identical for identical arguments
Pure_function
function ltrim(s) { sub(/^[ \t]+/, "", s); return s } function rtrim(s) { sub(/[ \t]+$/, "", s); return s } function trim(s) { return rtrim(ltrim(s));
Comparison of programming languages (string functions)
Comparison_of_programming_languages_(string_functions)
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
Decomposition of periodic functions
periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum
Fourier_series
Generalization of the Riemann zeta function for algebraic number fields
Dedekind zeta function of an algebraic number field K, usually denoted ζ K ( s ) {\displaystyle \zeta _{K}(s)} , is an analytic function that represents
Dedekind_zeta_function
Number of integers coprime to and less than n
zeta function as: ∑ n = 1 ∞ φ ( n ) n s = ζ ( s − 1 ) ζ ( s ) {\displaystyle \sum _{n=1}^{\infty }{\frac {\varphi (n)}{n^{s}}}={\frac {\zeta (s-1)}{\zeta
Euler's_totient_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
Hash function without any collisions
In computer science, a perfect hash function h for a set S is a hash function that maps distinct elements in S to a set of m integers, with no collisions
Perfect_hash_function
Function related to statistics and probability theory
likelihood is any function of θ equal to cPr[x | θ] for some positive value c. In maximum likelihood estimation, the model parameter(s) or argument that
Likelihood_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
Integral expressing the amount of overlap of one function as it is shifted over another
mathematical operation on two functions f and g that produces a third function f∗g, as the integral of the product of the two functions after one is reflected
Convolution
Type of subroutine in computer science
identity function whose domain and codomain are both the state space S {\displaystyle S} of the program, and for which: f ( s ) = s {\displaystyle f(s)=s} for
Null_function
Object whose state cannot be modified after it is created
A function of type const(S) function(const(T)) returns const(S) typed values for mutable, const and immutable arguments. In contrast, a function of type
Immutable_object
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
Sigmoid shape special function
mathematics, the error function (also called the Gauss error function), often denoted by e r f {\displaystyle \mathbf {erf} } , is the function erf ( z ) = 2
Error_function
Function whose actual domain of definition may be smaller than its apparent domain
mathematics, a partial function f from a set X to a set Y is a function from a subset S of X (possibly the whole X itself) to Y. The subset S, that is, the domain
Partial_function
Mathematical series
the constant unit function u(n), namely: ζ ( s ) = ∑ n = 1 ∞ 1 n s = ∑ n = 1 ∞ u ( n ) n s = D ( u , s ) , {\displaystyle \zeta (s)=\sum _{n=1}^{\infty
Dirichlet_series
Mathematical transform that expresses a function of time as a function of frequency
takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output
Fourier_transform
Ratio of polynomial functions
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator
Rational_function
Continuous function that is not absolutely continuous
In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in
Cantor_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 thermodynamics and statistical physics
partition function describes the statistical properties of a system in thermodynamic equilibrium.[citation needed] Partition functions are functions of the
Partition function (statistical mechanics)
Partition_function_(statistical_mechanics)
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
Hyperbolic analogues of trigonometric functions
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just
Hyperbolic_functions
Real function on a Euclidean space whose value depends only on distance from the origin
radial functions makes it possible also to define radial distributions. These are distributions S on R n {\displaystyle \mathbb {R} ^{n}} such that S [
Radial_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
Special mathematical function defined as sin(x)/x
In mathematics, physics and engineering, the sinc function (/ˈsɪŋk/), denoted by sinc(x), is defined as either sinc ( x ) = sin x x {\displaystyle
Sinc_function
Selberg zeta-function was introduced by Atle Selberg (1956). It is analogous to the famous Riemann zeta function ζ ( s ) = ∏ p ∈ P 1 1 − p − s {\displaystyle
Selberg_zeta_function
Set of all things that may be the input of a mathematical function
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom ( f ) {\displaystyle \operatorname
Domain_of_a_function
Multivalued function in mathematics
In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse
Lambert_W_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
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
Mathematical function
{\displaystyle \mathrm {c} } , s {\displaystyle \mathrm {s} } , n {\displaystyle \mathrm {n} } , and d {\displaystyle \mathrm {d} } . (Functions of the form pp (
Jacobi_elliptic_functions
Fourier transform of the probability density function
probability density function, then the characteristic function is the Fourier transform (with sign reversal) of the probability density function. Thus it provides
Characteristic function (probability theory)
Characteristic_function_(probability_theory)
Function whose domain is the positive integers
theory, an arithmetic, arithmetical, or number-theoretic function is generally any function whose domain is the set of positive integers and whose range
Arithmetic_function
Theorem in mathematics
mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function. The essential idea is that if
Inverse_function_theorem
Mathematical function relating circular and hyperbolic functions
hyperbolic functions of ψ {\textstyle \psi } and circular functions of ϕ . {\textstyle \phi .} s = tan 1 2 ϕ = tanh 1 2 ψ , 2 s 1 + s 2 = sin ϕ
Gudermannian_function
Averages of functions under the Dirichlet distribution
(Carlson) S-function is the Dirichlet average of e x {\displaystyle e^{x}} , S ( b , z ) = ∫ exp ( u ⋅ z ) d μ b ( u ) . {\displaystyle S(\mathbf {b}
Dirichlet_average
Topics referred to by the same term
Look up lambda function in Wiktionary, the free dictionary. Lambda function may refer to: Dirichlet lambda function, λ(s) = (1 – 2−s)ζ(s) where ζ is the
Lambda_function
Functional programming language
lambda operator or free variables. It relies mainly on two built-in functions (s and k) and an apply operator (written `, the backquote character). These
Unlambda
Nearest integers from a number
Floor and ceiling functions In mathematics, the floor function is the function that takes a real number x as input and returns the greatest integer less
Floor_and_ceiling_functions
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
Function used as a performance test problem for optimization algorithms
In mathematical optimization, the Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is used as a performance
Rosenbrock_function
Probability of survival beyond any specified time
survival function or reliability function is: S ( t ) = ∫ t ∞ f ( u ) d u = Pr ( T > t ) = 1 − F ( t ) = 1 − ∫ 0 t f ( u ) d u {\displaystyle S(t)=\int
Survival_function
Type of energy
In solid-state physics, the work function is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the
Work_function
Effect in signal processing
The Fourier transform of a function of time, s(t), is a complex-valued function of frequency, S(f), often referred to as a frequency spectrum. Any linear
Spectral_leakage
given by the Lommel functions s μ , ν ( z ) {\displaystyle s_{\mu ,\nu }(z)} and S μ , ν ( z ) {\displaystyle S_{\mu ,\nu }(z)} : s μ , ν ( z ) = π 2 (
Lommel_function
Mathematical function
Riemann zeta function ζ ( s ) {\displaystyle \zeta (s)} implies that log ζ ( s ) = ∑ n > 0 P ( n s ) n , {\displaystyle \log \zeta (s)=\sum _{n>0}{\frac
Prime_zeta_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
Piecewise function that clamps its input to be non-negative
x − s ) f ″ ( s ) d s for a < x < b . {\displaystyle f(x)=f(a)+(x-a)f'(a)+\int _{a}^{b}R(x-s)f''(s)\,ds\quad {\mbox{for }}a<x<b.} Ramp function has the
Ramp_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
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S FUNCTION
S FUNCTION
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S FUNCTION
S FUNCTION
S FUNCTION
S FUNCTION
S FUNCTION
S FUNCTION
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