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Certain convolution formulas for multiple series

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Abstract

In this paper, computing a double integral of convolution type in two ways, we give certain formulas for general multiple series. The method is based on that of Kanemitsu–Tanigawa–Yoshimoto in their previous work. As concrete examples, considering multiple zeta-functions of Barnes type and Euler–Zagier type, and Epstein zeta-functions, we give new formulas for multiple series involving these zeta-functions.

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Acknowledgements

The author would like to express his sincere gratitude to the referee who read this paper carefully, pointed out several insufficient points and gave valuable suggestions and comments.

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Authors and Affiliations

  1. Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo, 192-0397, Japan

    Hirofumi Tsumura

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  1. Hirofumi Tsumura
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Correspondence to Hirofumi Tsumura.

Additional information

This research was partially supported by Grant-in-Aid for Science Research (No. 23540022), Japan Society for the Promotion of Science.

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Tsumura, H. Certain convolution formulas for multiple series. Ramanujan J 32, 353–369 (2013). https://doi.org/10.1007/s11139-012-9453-z

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  • DOI: https://doi.org/10.1007/s11139-012-9453-z

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