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Some Families of Series Representations for the Riemann ζ(3)

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Abstract

This paper presents a systematic investigation of several classes of (known or new) series representations for the Riemann Zeta function ζ (s) when s = 3. The rates of convergence of some of these series are comparable favorably with that of the series used earlier in proving the irrationality of ζ(3). A double hypergeometric series transformation is obtained as a by-product.

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Authors and Affiliations

  1. Institute of Mathematics Academia Sinica, Taipei, 11529, Taiwan, Republic of China

    Ming-Po Chen

  2. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, V8W 3P4, Canada

    H.M. Srivastava

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  1. Ming-Po Chen
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  2. H.M. Srivastava
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Correspondence to Ming-Po Chen.

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23 June 1941 - 09 December 1997

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Chen, MP., Srivastava, H. Some Families of Series Representations for the Riemann ζ(3). Results. Math. 33, 179–197 (1998). https://doi.org/10.1007/BF03322082

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