Reduction Formulae for Karlsson–minton Type Hypergeometric Functions
نویسنده
چکیده
We prove a master theorem for hypergeometric functions of Karlsson–Minton type, stating that a very general multilateral U(n) Karlsson–Minton type hypergeometric series may be reduced to a finite sum. This identity contains the Karlsson–Minton summation formula and many of its known generalizations as special cases, and it also implies several “Bailey-type” identities for U(n) hypergeometric series, including multivariable 10W9 transformations of Milne and Newcomb and of Kajihara. Even in the one-variable case our identity is new, and even in this case its proof depends on the theory of multivariable hypergeometric series.
منابع مشابه
KARLSSON–MINTON TYPE HYPERGEOMETRIC FUNCTIONS ON THE ROOT SYSTEM Cn
which holds for mi non-negative integers and Re (a + |m|) < 1. Accordingly, hypergeometric series with integral parameter differences have been called Karlsson–Minton type hypergeometric series; other results for such series may be found in [C, G1, G2, S1, S2]. In recent work [R], we have derived a very general reduction formula for series of Karlsson–Minton type. We recall it in its most gener...
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