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Evaluation of infinite series involving special products and their algebraic characterization. (English) Zbl 1209.11067

The main result of this paper is a general summation for a special hypergeometric series. As an application several interesting expressions for \(\pi\) are demonstrated. Some criteria for the sums of the series to be transcendental are included. The proofs are based on the expressions of the special integrals.

MSC:

11J81 Transcendence (general theory)
33C20 Generalized hypergeometric series, \({}_pF_q\)
11J91 Transcendence theory of other special functions
33B15 Gamma, beta and polygamma functions
33F05 Numerical approximation and evaluation of special functions
40C10 Integral methods for summability
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