In mathematics, generalized functions are objects extending the notion of functions on real or complex numbers. There is more than one recognized theory...

mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of n. The...

In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing...

(\operatorname {sgn} 0)^{2}=0} . This generalized signum allows construction of the algebra of generalized functions, but the price of such generalization...

vector/tuple-valued function in this generalized scheme, in which case this is precisely the standard definition of function composition. A set of finitary...

{\displaystyle 1/p!} in § Properties of the generalized Kronecker delta below disappearing. In terms of the indices, the generalized Kronecker delta is defined as:...

mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value...

arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus, a function f {\displaystyle f} defined on a subset...

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...

smooth functions, used for example in distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution...

In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with...

points with non-zero charge). The Dirac delta function, or δ function, is (informally) a generalized function on the real number line that is zero everywhere...

paragraphs 23.8 and 23.32) Gel'fand, I. M.; Vilenkin, N. Ya (1964). Generalized Functions: Applications of Harmonic Analysis. Burlington: Elsevier Science...

singularity Generalized function Distribution Minkowski's question-mark function (**) This condition depends on the references "Singular function", Encyclopedia...

formula. Remark: Most rigorously, multiplication of the rect function with a generalized function, such as the Dirac comb, fails. This is due to undetermined...

distributions are a kind of generalized function in mathematical analysis. Distributions make it possible to differentiate functions whose derivatives do not...

Multiscale Green's function (MSGF) is a generalized and extended version of the classical Green's function (GF) technique for solving mathematical equations...

+1-x\right)y'+n\,y=0} are called generalized Laguerre polynomials, or associated Laguerre polynomials. One can also define the generalized Laguerre polynomials recursively...

the theory of generalized functions, published by Laurent Schwartz in 1952. It states, in broad terms, that the generalized functions introduced by Schwartz...

logistic function and generalizations. In growth modeling, numerous generalizations exist, including the generalized logistic curve, the Gompertz function, the...

examples can be unified and generalized by considering a multiset E, and finite sub-multisets S and T of E. The Möbius function is μ ( S , T ) = { 0 if ...

The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows...

(2001) [1994], "Generalized function", Encyclopedia of Mathematics, EMS Press. Vladimirov, V.S. (2001) [1994], "Generalized functions, space of", Encyclopedia...

the wave front (set) WF(f) characterizes the singularities of a generalized function f, not only in space, but also with respect to its Fourier transform...

zeta-functions, it is known as the extended Riemann hypothesis (ERH) and when it is formulated for Dirichlet L-functions, it is known as the generalized Riemann...

In statistics, the generalized Pareto distribution (GPD) is a family of continuous probability distributions. It is often used to model the tails of another...

Complex function Function (mathematics) Generalized function List of special functions and eponyms List of types of functions Rational function Special...

of smooth functions with compact support is the construction of so-called mollifiers, which are important in theories of generalized functions, such as...

function when ⁠ σ 2 = 0 {\displaystyle \sigma ^{2}=0} ⁠. However, one can define the normal distribution with zero variance as a generalized function;...

The rectangular function (also known as the rectangle function, rect function, Pi function, Heaviside Pi function, gate function, unit pulse, or the normalized...