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{{short description|Form of Gaussian quadrature}} In [[numerical analysis]], '''Gauss–Hermite quadrature''' is a form of [[Gaussian quadrature]] for approximating the value of integrals of the following kind ...

[[Image:DawsonDp.svg|thumb|300px|right|The Dawson function, <math>F(x) = D_+(x)</math>, around the origin]] [[Image:DawsonDm.svg|thumb|300px|right|The Dawson function, <math>D_-(x)</math>, around the origin]] ...

...very nearly 3.6. The black and red profiles are the limiting cases of the Gaussian (γ =0) and the Lorentzian (σ =0) profiles respectively. </small>| ...chy distribution|Cauchy-Lorentz distribution]] and a [[Normal distribution|Gaussian distribution]]. It is often used in analyzing data from [[spectroscopy]] or ...

...square period lattice and is closely related to the [[Weierstrass elliptic function]] when the Weierstrass invariants satisfy {{math|''g''₂ {{=}} 1 ...n more algebraic terms, the [[period lattice]] is a real multiple of the [[Gaussian integer]]s. ...

{{Redirect|Gaussian integration|the integral of a Gaussian function|Gaussian integral}} ...en 2-point Gaussian and trapezoidal quadrature.|Comparison between 2-point Gaussian and trapezoidal quadrature. ...

...al polynomials]] on the interval [&minus;1,1] with respect to the [[weight function]] (1&nbsp;&minus;&nbsp;''x''²)^''α''–1/2. They general * The polynomials can be defined in terms of their [[generating function]] {{harv|Stein|Weiss|1971|loc=§IV.2}}: ...

[[File:Error Function.svg|thumb|right|400px|Plot of the error function]] ...the '''Gauss error function'''), often denoted by '''erf''', is a complex function of a complex variable defined as:<ref>{{cite book|last =Andrews|first = Lar ...

{{Short description|Special function defined by an integral}} ...esnel]] that are used in [[optics]] and are closely related to the [[error function]] (erf). They arise in the description of [[near and far field|near-field]] ...

* in [[numerical analysis]] as [[Gaussian quadrature]]; * in [[systems theory]] in connection with nonlinear operations on [[Gaussian noise]]. ...

{{For|other generalizations of the hypergeometric function|Hypergeometric function}} {{distinguish|general hypergeometric function}} ...

...ction]]s, Legendre functions of the second kind, and [[associated Legendre function]]s. ...polynomials are defined as an orthogonal system with respect to the weight function <math>w(x) = 1</math> over the interval <math> [-1,1]</math>. That is, <mat ...

More generally, a '''Laguerre function''' is a solution when {{mvar|n}} is not necessarily a non-negative integer. The Laguerre polynomials are also used for [[Gaussian quadrature]] to numerically compute integrals of the form ...

| [[Bessel function#math.51.18| Bessel function]] "title": "Bessel function", ...

{{Short description|Extension of the factorial function}} ...eblen function|the gamma distribution in statistics|Gamma distribution|the function used in video and image color representations|Gamma correction}} ...

{{Short description|Multivalued "function"}} {{DISPLAYTITLE:Lambert ''W'' function}} ...

...ctions with arbitrary real or complex values of ℓ and ''m'' are [[Legendre function]]s. In that case the parameters are usually labelled with Greek letters. {{main|Legendre function}} ...

{{Short description|Special function defined by a hypergeometric series}} ...ergeometric function" sometimes refers to the [[generalized hypergeometric function]]. For other hypergeometric functions see [[#See also|See also]].}} ...

...ation that is close to the best polynomial approximation to a [[continuous function]] under the [[maximum norm]], also called the "[[minimax]]" criterion. This The [[generating function|ordinary generating function]] for {{mvar|T_n}} is ...