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WZ-proofs of “divergent” Ramanujan-type series. (English) Zbl 1285.11151

Kotsireas, Ilias S. (ed.) et al., Advances in combinatorics. In part based on the 3rd Waterloo workshop on computer algebra (WWCA, W80) 2011, Waterloo, Canada, May 26–29, 2011. Dedicated to Herbert Saul Wilf on the occasion of his 80th birthday. Berlin: Springer (ISBN 978-3-642-30978-6/hbk; 978-3-642-30979-3/ebook). 187-195 (2013).
Summary: We prove some “divergent” Ramanujan-type series for \(1/\pi\) and \(1/\pi^2\) applying a Barnes-integrals strategy of the WZ-method. In addition, in the last section, we apply the WZ-duality technique to evaluate some convergent related series.
For the entire collection see [Zbl 1271.05001].

MSC:

11Y60 Evaluation of number-theoretic constants
33C20 Generalized hypergeometric series, \({}_pF_q\)
33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)

Software:

EKHAD
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