A proof of Kummer’s theorem
نویسنده
چکیده
Following suggestions of T. H. Koornwinder [3], we give a new proof of Kummer’s theorem involving Zeilberger’s algorithm, the WZ method and asymptotic estimates. In the first section, we recall a classical proof given by L. J. Slater [7]. The second section discusses the new proof, in the third section sketches of similar proofs for Bailey’s and Dixon’s theorems are given. The author is grateful to Peter Paule for his helpful comments. 1 Slater’s proof In classical hypergeometric theory, formulae concerning summation, transformation and contiguous relations are provided in order to manipulate expressions that represent special functions. One of those is Kummer’s non-terminating summation theorem: 2F1 [
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