## 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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