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

Guillera, Jesús

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.)

Keywords:

hypergeometric series; WZ-method; Ramanujan-type series for \(1/\pi\) and \(1/\pi^2\); Barnes integrals

Software:

EKHAD