Terminating \(_2F_1(4)\)-series perturbed by two integer parameters. (English) Zbl 1352.33001
Summary: By means of generating functions and the linearization method, we establish analytical formulae for a class of terminating \( _2F_1(4)\)-series perturbed by two integer parameters. Under the Pfaff transformation, these formulae confirm, unexpectedly, a conjecture about evaluation of the \( _2F_1(-3)\)-series made by M. Apagodu and D. Zeilberger [Integers 8, No. 1, Article A36, 6 p. (2008; Zbl 1210.33024)].
MSC:
33C20 | Generalized hypergeometric series, \({}_pF_q\) |
05A19 | Combinatorial identities, bijective combinatorics |
Keywords:
terminating hypergeometric series; generating function; linearization method; Chu-Vandermonde formula; Kummer’s summation theorem; Pfaff transformationCitations:
Zbl 1210.33024Software:
BruteTwoFoneReferences:
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