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Single variable hypergeometric functions pFq arise in connection with thepower series solution of the Schrodinger equation or in the summation ofperturbation expansions in quantum mechanics. For these applications, it is ofinterest to obtain analytic expressions, and we present the reduction of anumber of cases of pFp and p+1F_p, mainly for p=2 and p=3. These and relatedseries have additional applications in quantum and statistical physics andchemistry.Comment: 17 pages, no figure

ON HYPERGEOMETRIC SERIES REDUCTIONS FROM INTEGRAL REPRESENTATIONS, THE KAMPÉ DE FÉRIET FUNCTION AND ELSEWHERE