The Campé de Ferrier function is a generalized hypergeometric function of two variables, introduced into circulation by the French mathematician Joseph Campe de Ferrier and named in his honor:
- {\ displaystyle {} ^ {p + q} f_ {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 ^ {m} y ^ {n}} {m! n!}}.}
Notes
- Exton, Harold (1978), Handbook of hypergeometric integrals , Mathematics and its Applications, Chichester: Ellis Horwood Ltd., ISBN 978-0-85312-122-0 , < https://books.google.com/books?id= fUHvAAAAMAAJ >
- Kampé de Fériet, MJ (1937), La fonction hypergéométrique. , vol. 85, Mémorial des sciences mathématiques, Paris: Gauthier-Villars , < https://books.google.com/books?id=JObuAAAAMAAJ >
- Ragab, FJ Expansions of Kampe de Feriet's double hypergeometric function of higher order ( Journal ) // Journal für die reine und angewandte Mathematik | J. f. reine angew. Mathem. : journal. - 1963. - No. 212 . - P. 113-119 . - DOI : 10.1515 / crll.1963.212.113 .
Links
- Weisstein, Eric W. Function Campe de Ferrier (English) on the site Wolfram MathWorld .