Search results

...defined from [[analytic function]]s <math>B</math> and <math>C</math> by [[generating function]]s of the form ...last2=Buck | first2=R. Creighton | title=Polynomial expansions of analytic functions | url=https://books.google.com/books?id=eihMuwkh4DsC | publisher=[[Springer ...

...</sub>, which are special cases of [[generalized Appell polynomials]] with generating function of the form ...e | first1=W. C. | authorlink=William Charles Brenke | title=On generating functions of polynomial systems | mr=0012720 | year=1945 | journal=[[American Mathema ...

===Ordinary generating functions=== It is also possible to demonstrate the theorem through the use of [[ordinary generating function]]s of the binomial distribution: ...

...me{\delta}_{n,m}</math> is the [[Kronecker delta function]] and the weight functions are ==Generating functions== ...

...'''primitive recursive set functions''' or '''primitive recursive ordinal functions''' are analogs of [[primitive recursive function]]s, defined for [[Set (mat ...function]] from sets to sets that can be obtained from the following basic functions by repeatedly applying the following rules of substitution and recursion: ...

==Generating function== [[Category:Special hypergeometric functions]] ...

==Generating functions== The continuous Hahn polynomials have the following generating function:<ref>Koekoek, Lesky, & Swarttouw (2010), p. 202.</ref> ...

* Panholzer and Prodinger's proof via [[generating functions]]; | title = A generating functions proof of a curious identity ...

...oblem in [[combinatorics|combinatorial]] [[mathematics]] that involves a [[generating function]]. In this problem, a ''fountain'' is an arrangement of non-overla ...oblem is then given by the coefficients of the polynomial of the following generating function: ...

...) are polynomials introduced by {{harvtxt|Rainville|1945}} given by the [[generating function]] ...last2=Buck | first2=R. Creighton | title=Polynomial expansions of analytic functions | url=https://books.google.com/books?id=eihMuwkh4DsC | publisher=[[Springer ...

===Ordinary generating functions=== ...polynomials allows to give simple equations for the [[ordinary generating functions]] (OGF) of many natural questions. ...

{{Short description|Generating pseudo-random numbers that follow a probability distribution}} ...dom number sampling''' is the [[Numerical analysis|numerical]] practice of generating [[pseudo-random number]]s (PRN) that follow a given [[probability distribut ...

...sion is to be made. We require a proof which will not appeal to generating functions, . . . ".<ref name=Dyson/> Dyson introduced the idea of rank of a partition == Generating functions == ...

...uerre polynomials]] introduced by {{harvtxt|Denisyuk|1954}} given by the [[generating function]]{{sfnp|Boas|Buck|1958|p=41}} |title = Polynomial expansions of analytic functions ...

...quence to express formulas for the series coefficients of a given ordinary generating function. ...notation for coefficient extraction usually applied to formal [[generating functions]] in some complex variable, by denoting <math>[n^{-s}] D_f(s) =: f(n)</math ...

== Generating functions == Then, the [[probability generating function]], [[moment generating function]] and [[characteristic function]] are given, respectively, by:<ref ...

...totic estimates]] for the coefficients of [[Generating_function|generating functions]].<ref>Melczer 2021, pp. vii and ix.</ref><ref>Pemantle and Wilson 2013, pp ...on#Bivariate_and_multivariate_generating_functions|multivariate generating functions]] started in the 1970s using probabilistic methods.<ref>Melczer 2021, pp. 1 ...

...mbert|year=1921|authorlink=Pierre Humbert (mathematician)}} given by the [[generating function]] ...last2=Buck | first2=R. Creighton | title=Polynomial expansions of analytic functions | url=https://books.google.com/books?id=eihMuwkh4DsC | publisher=[[Springer ...

...ed case, where we have a set of labelled objects given by an [[exponential generating function]] (EGF) ''g''(''z'') which are being distributed into ''n'' slots ...the functions <math>f_n(z)</math> can be further combined into a single [[generating function]]: ...

...ynomials also have a representation in terms of generalized hypergeometric functions, namely ===Generating function=== ...