In mathematics, the Kampé de Fériet function is a two-variable generalization of the

generalized hypergeometric series In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by ''n'' is a rational function of ''n''. The series, if convergent, defines a generalized hypergeometric function, wh ...

, introduced by

Joseph Kampé de Fériet Marie-Joseph Kampé de Fériet (Paris, 14 May 1893 – Villeneuve d'Ascq, 6 April 1982) was professor at Université Lille Nord de France from 1919 to 1969. Besides his works on mathematics and fluid mechanics, he directed the ''Institut de mé ...

. The Kampé de Fériet function is given by :

^F_\left(
\begin
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
x,y\right)=
\sum_^\infty\sum_^\infty\frac\frac\cdot\frac.

Applications

The general sextic equation can be solved in terms of Kampé de Fériet functions.Mathworld - Sextic Equation
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References

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External links

* Hypergeometric functions {{analysis-stub