Guardat en:
| Autor principal: | |
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| Format: | Preprint |
| Publicat: |
2002
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/math/0201024 |
| Etiquetes: |
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Taula de continguts:
- 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.