Kampé de Fériet function - Alchetron, the free social encyclopedia

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

The Kampé de Fériet function is given by

p + q F r + s ( 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 ! .

Applications

The general sextic equation can be solved in terms of Kampé de Fériet functions.

References

Kampé de Fériet function Wikipedia

(Text) CC BY-SA