An Apéry-like difference equation for Catalan's constant
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arXiv
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| Format: | Preprint |
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2002
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| _version_ | 1866911217355849728 |
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| author | Zudilin, Wadim |
| author_facet | Zudilin, Wadim |
| contents | 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 $ζ(4)=π^4/90$, and we announce corresponding results at the end of this paper. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_math_0201024 |
| institution | arXiv |
| publishDate | 2002 |
| record_format | arxiv |
| spellingShingle | An Apéry-like difference equation for Catalan's constant Zudilin, Wadim Number Theory Numerical Analysis Classical Analysis and ODEs Primary 39A05, 11B37, 11J70; Secondary 33C20, 33C60, 11B65, 11M06 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 $ζ(4)=π^4/90$, and we announce corresponding results at the end of this paper. |
| title | An Apéry-like difference equation for Catalan's constant |
| topic | Number Theory Numerical Analysis Classical Analysis and ODEs Primary 39A05, 11B37, 11J70; Secondary 33C20, 33C60, 11B65, 11M06 |
| url | https://arxiv.org/abs/math/0201024 |