- Title
- An Apéry-like difference equation for Catalan's constant
- Creator
- Zudilin, W.
- Relation
- The Electronic Journal of Combinatorics Vol. 10
- Relation
- http://www.combinatorics.org/ojs/index.php/eljc/issue/archive
- Publisher
- Electronic Journal of Combinatorics
- Resource Type
- journal article
- Date
- 2003
- Description
- 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 derive a new way of fast calculation of Catalan’s constant as well as a new continued-fraction expansion for it. Similar arguments are put forward to deduce a second-order difference equation and a new continued fraction for ζ(4) = π⁴/90.
- Subject
- Catalan's constant; Apéry; difference equation; hypergeometric series
- Identifier
- http://hdl.handle.net/1959.13/934895
- Identifier
- uon:11934
- Identifier
- ISSN:1077-8926
- Language
- eng
- Full Text
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