Abstract
In this paper, we show certain formulas for double series involving hyperbolic functions which come from the well-known transformation formula, namely Jacobi’s identity for the classical theta function. These can be regarded as relevant analogues of formulas given in the previous papers.
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Acknowledgements
The author deeply thanks the referee for his/her valuable suggestion, and also wishes to express his sincere gratitude to Professors Yohei Tachiya and Hajime Kaneko for their valuable comments on values of the theta function and their properties.
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This work was also supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C) 15K04788.
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Tsumura, H. Double Series Identities Arising from Jacobi’s Identity of the Theta Function. Results Math 73, 10 (2018). https://doi.org/10.1007/s00025-018-0770-4
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DOI: https://doi.org/10.1007/s00025-018-0770-4