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In mathematics, the '''Kampé de Fériet function''' is a two-variable generalization of the [[hypergeometric series]], introduced by [[Marie-Joseph Kampé de Fériet]].


The Kampé de Fériet function is given by
:<math>
{}^{p+q}f_{r+s}\left(
\begin{matrix}
a_1,\cdots,a_p\colon b_1,b_1{}';\cdots;b_q,b_q{}'; \\
c_1,\cdots,c_r\colon d_1,d_1{}';\cdots;d_s,d_s{}';
\end{matrix}
x,y\right)=
\sum_{m=0}^\infty\sum_{n=0}^\infty\frac{(a_1)_{m+n}\cdots(a_p)_{m+n}}{(c_1)_{m+n}\cdots(c_r)_{m+n}}\frac{(b_1)_m(b_1{}')_n\cdots(b_q)_m(b_q{}')_n}{(d_1)_m(d_1{}')_n\cdots(d_s)_m(d_s{}')_n}\cdot\frac{x^my^n}{m!n!}.
</math>


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==References==
*{{Citation | last1=Exton | first1=Harold | authorlink=Harold Exton | title=Handbook of hypergeometric integrals | url=http://books.google.com/books?id=fUHvAAAAMAAJ | publisher=Ellis Horwood Ltd. | location=Chichester | series=Mathematics and its Applications | isbn=978-0-85312-122-0 | mr=0474684 | year=1978}}
*{{Citation | last1=Kampé de Fériet | first1=M. J. | title=La fonction hypergéométrique. | url=http://books.google.com/books?id=JObuAAAAMAAJ | publisher=Paris: Gauthier-Villars | language=French | series=Mémorial des sciences mathématiques | jfm=63.0996.03 | year=1937 | volume=85}}
* {{ cite journal
|first1=F. J.
|last1=Ragab
|title = Expansions of Kampe de Feriet's double hypergeometric function of higher order
|year=1963
|issue=212
|pages=113–119
|doi=10.1515/crll.1963.212.113
|journal=[[Crelle's Journal|J. f. reine angew. Mathem.]]
}}
 
==External links==
*{{MathWorld |title=Kampé de Fériet function |id=KampedeFerietFunction}}
 
{{DEFAULTSORT:Kampe de Feriet function}}
[[Category:Hypergeometric functions]]
 
 
{{analysis-stub}}

Revision as of 20:53, 6 March 2013

In mathematics, the Kampé de Fériet function is a two-variable generalization of the hypergeometric series, introduced by Marie-Joseph Kampé de Fériet.

The Kampé de Fériet function is given by

References

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