查看“︁Kampé de Fériet函数”︁的源代码

'''Kampé de Fériet函数'''是[[法兰西]][[数学家]]{{le|Joseph Kampé de Fériet}}在1937年为推广[[广义超几何函数]]而创建的二元[[特殊函数]]，将同样是二元函数的[[阿佩尔函数|阿佩尔超几何函数]]作为它的特殊情形，其定义如下：

:<math>
F^{p,q}_{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>

==应用==
一般的[[六次方程]]可以通过Kampé de Fériet函数求解。

Kampé de Fériet函数也可以用来表示[[广义超几何函数]]对某个参数的[[导数]]，或是两到三个[[Meijer_G-函数]]的[[不定积分]]。（如同其他超几何函数一样，单个Meijer_G-函数的不定积分可以用自身表示）

==参考文献==
*{{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 | accessdate=2015-04-04 | archive-date=2014-06-28 | archive-url=https://web.archive.org/web/20140628115954/http://books.google.com/books?id=fUHvAAAAMAAJ | dead-url=no }}
*{{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=fr | series=Mémorial des sciences mathématiques | jfm=63.0996.03 | year=1937 | volume=85 | accessdate=2015-04-04 | archive-date=2014-06-28 | archive-url=https://web.archive.org/web/20140628115626/http://books.google.com/books?id=JObuAAAAMAAJ | dead-url=no }}
* {{ 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.]]
}}

==外部链接==
*{{MathWorld |title=Kampé de Fériet function |id=KampedeFerietFunction}}


[[Category:超几何函数]]