An Apéry-like difference equation for Catalan's constant

Details An Apéry-like difference equation for Catalan's constant An Apéry-like difference equation for Catalan's constant

2002-01-04

arxiv.org/abs/math/0201024v3

Electron. J. Combin. 10:1 (2003), #R14, 10 pages

Mathematics

Number Theory

10 pages; updating references (28 October 2002)

Scientific paper

Applying Zeilberger's algorithm of creative telescoping to a family of certain very-well-poised hypergeometric series involving linear forms in Catalan's constant with rational coefficients, we obtain a second-order difference equation for these forms and their coefficients. As a consequence we obtain a new way of fast calculation of Catalan's constant as well as a new continued-fraction expansion for it. Similar arguments can be put forward to indicate a second-order difference equation and a new continued fraction for $\zeta(4)=\pi^4/90$, and we announce corresponding results at the end of this paper.

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