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...function]]<ref>Gelb, A., and W. E. Vander Velde: Multiple-Input Describing Functions and Nonlinear System Design, McGraw Hill, 1968.</ref> which describe the re ...that <math> |U(\omega_0)|=\gamma </math> yields the definition of the k-th order HOSIDF: ...

...called '''Riesz–Sobolev''' inequality, states that any three non-negative functions <math>f : \mathbb{R}^n \to \mathbb{R}^+</math>, <math>g : \mathbb{R}^n \to ...\mathbb{R}^+</math> are the [[symmetric decreasing rearrangement]]s of the functions <math>f</math>, <math>g</math> and <math>h</math> respectively. ...

...andard notation for the family of subsets with a given order type. Jónsson functions are named for [[Bjarni Jónsson]]. ...for this special case there is a simpler proof of the existence of Jónsson functions. {{harvs|txt|authorlink=Fred Galvin|last=Galvin|last2= Prikry|year=1976}} g ...

...is a method used to [[derivative|differentiate]] [[function (mathematics)|functions]] by employing the [[logarithmic derivative]] of a function {{math|''f''}}, ...entiation of almost all [[differentiable function]]s, providing that these functions are non-zero. ...

In [[celestial mechanics]], the '''Stumpff functions''' <math>\ c_k(x)\ ,</math> were developed by [[Karl Stumpff]] for analyzin ...]], [[cosine]], and [[exponential function|exponential]] functions, Stumpf functions are well-behaved ''[[entire function]]s''&nbsp;: Their [[series (mathematic ...

...right, and there exists an exterior derivative. Correspondingly, a first order quantum differential calculus means at least the following: ...t says that the only functions killed by <math>{\rm d}</math> are constant functions. ...

{{short description|The only quadratic pairing functions are the Cantor polynomials}} == Higher dimensions == ...

...a [[real function]] is '''flat''' at <math>x_0</math> if all its [[higher-order derivative|derivatives]] at <math>x_0</math> exist and equal {{math|0}}. [[Category:Smooth functions]] ...

...|issue=3 |pages=347–382 }}</ref> or some [[Second-order arithmetic|higher-order arithmetics]]. ...y be denoted <math>{\mathrm {AC}}!</math>. It may also only be adopted for functions from the naturals to the naturals, then called <math>{\mathrm {AC}_{00}}!</ ...

...he image of [[Gaussian function]]s under the Weil–Brezin map are nil-theta functions, which are related to [[theta function]]s. The Weil–Brezin map is sometimes ==Nil-theta functions== ...

...the [[Eisenstein series]]. Another example is the [[Weierstrass's elliptic functions#Modular discriminant|&Delta; function]]. == Higher levels == ...

==First order Cauchy–Kovalevskaya theorem== ...e [[analytic function]]s. The theorem and its proof are valid for analytic functions of either real or complex variables. ...

...d radicals in order to express the solutions to equations of the fifth and higher degrees. In 1858, [[Charles Hermite]], [[Leopold Kronecker]], and [[Frances ...urth degree and below. Something more general is required for equations of higher degree, so to solve the quintic, Hermite, et al. replaced the exponential b ...

Based on the key idea of [[higher-order singular value decomposition]]<ref name=Lath00>{{cite journal ...and Yam proposed the concept of '''HOSVD-based [[canonical form]]''' of TP functions and quasi-LPV system models.<ref name=canon1>{{cite conference ...

...>\log^+(x)=\max[0,\log(x)]</math>. Being the ratio of two bounded analytic functions is a sufficient condition for a function to be of bounded type (defined in Functions of bounded type are not necessarily bounded, nor do they have a property ca ...

...aring]], is a first-order model of shape deformation, tapering is a higher order deformation just as twisting and bending. Tapering can be thought of as non let ''a'' and ''b'' be functions of ''z'' so that: ...

...ns of different random variables are sometimes called '''cross-correlation functions''' to emphasize that different variables are being considered and because t Correlation functions are a useful indicator of dependencies as a function of distance in time or ...

The general [[sextic equation]] can be solved in terms of Kampé de Fériet functions.<ref name="Mathworld - Sextic Equation">[http://mathworld.wolfram.com/Sexti ...= Expansions of Kampe de Feriet's double hypergeometric function of higher order ...

...me=Stromberg>Janos-Olov Strömberg, ''A modified Franklin system and higher order spline systems on Rⁿ as unconditional bases for [[Hardy space]]s ...sub> = ''A''₀ &cup; { 1/2 } then the '''Strömberg wavelet''' of order ''m'' is a function ''S''^''m''(''t'') satisfying the following c ...

[[Category:Higher-order functions]] ...