Runhuan Feng, Alexey Kuznetsov, Fenghao Yang
Published 2015-12-03Version 1
The list of known identities involving finite sums of products of hypergeometric functions is quite short. In this paper we extend the number of such results and we derive new families of identities for finite sums of products of two generalized hypergeometric (or two generalized q-hypergeometric) functions. The proof of these results is based on the non-local derangement identity.
Addition formulas for the $_{p}F_{p}$ and $_{p+1}F_{p}$ generalized hypergeometric functions with arbitrary parameters and their Kummer- and Euler-type transformations
A new identity for a sum of products of the generalized hypergeometric functions
Newton diagram of positivity for ${}_1F_2$ generalized hypergeometric functions
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