Kampé de Fériet函数维基百科,自由的 encyclopedia Kampé de Fériet函数是法兰西数学家Joseph Kampé de Fériet(英语: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超几何函数作为它的特殊情形,其定义如下: F r , s p , q ( a 1 , ⋯ , a p : b 1 , b 1 ′ ; ⋯ ; b q , b q ′ ; c 1 , ⋯ , c r : d 1 , d 1 ′ ; ⋯ ; d s , d s ′ ; x , y ) = ∑ m = 0 ∞ ∑ n = 0 ∞ ( a 1 ) m + n ⋯ ( a p ) m + n ( c 1 ) m + n ⋯ ( c r ) m + n ( b 1 ) m ( b 1 ′ ) n ⋯ ( b q ) m ( b q ′ ) n ( d 1 ) m ( d 1 ′ ) n ⋯ ( d s ) m ( d s ′ ) n ⋅ x m y n m ! n ! . {\displaystyle F_{r,s}^{p,q}\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^{m}y^{n}}{m!n!}}.}
Kampé de Fériet函数是法兰西数学家Joseph Kampé de Fériet(英语: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超几何函数作为它的特殊情形,其定义如下: F r , s p , q ( a 1 , ⋯ , a p : b 1 , b 1 ′ ; ⋯ ; b q , b q ′ ; c 1 , ⋯ , c r : d 1 , d 1 ′ ; ⋯ ; d s , d s ′ ; x , y ) = ∑ m = 0 ∞ ∑ n = 0 ∞ ( a 1 ) m + n ⋯ ( a p ) m + n ( c 1 ) m + n ⋯ ( c r ) m + n ( b 1 ) m ( b 1 ′ ) n ⋯ ( b q ) m ( b q ′ ) n ( d 1 ) m ( d 1 ′ ) n ⋯ ( d s ) m ( d s ′ ) n ⋅ x m y n m ! n ! . {\displaystyle F_{r,s}^{p,q}\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^{m}y^{n}}{m!n!}}.}