mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, 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, which ...

, introduced by

Joseph Kampé de Fériet Marie-Joseph Kampé de Fériet (14 May 1893 – 6 April 1982) was a French mathematician at Université Lille Nord de France from 1919 to 1969. Besides his works on mathematics and fluid mechanics, he directed the ''Institut de mécanique des flui ...

. 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 In algebra, a sextic (or hexic) polynomial is a polynomial of degree six. A sextic equation is a polynomial equation of degree six—that is, an equation whose left hand side is a sextic polynomial and whose right hand side is zero. More precise ...

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

* * *

External links

* Hypergeometric functions {{analysis-stub

Applications

See also

References

External links