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Hypergeometric rational approximations to ζ(4)

Published online by Cambridge University Press:  03 February 2020

Raffaele Marcovecchio
Affiliation:
Dipartimento di Ingegneria e Geologia, Università di Chieti-Pescara, Viale Pindaro, 42, 65127Pescara, Italy (raffaele.marcovecchio@unich.it)
Wadim Zudilin
Affiliation:
Department of Mathematics, IMAPP, Radboud University, PO Box 9010, 6500GL Nijmegen, Netherlands (w.zudilin@math.ru.nl)
Corresponding
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Abstract

We give a new hypergeometric construction of rational approximations to ζ(4), which absorbs the earlier one from 2003 based on Bailey's 9F8 hypergeometric integrals. With the novel ingredients we are able to gain better control of the arithmetic and produce a record irrationality measure for ζ(4).

Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Edinburgh Mathematical Society 2020

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