Abstract
As in our previous work [14], a function is said to be of theta-type when its asymptotic behavior near any root of unity is similar to what happened for Jacobi theta functions. It is shown that only four Euler infinite products have this property. That this is the case is obtained by investigating the analyticity obstacle of a Laplace-type integral of the exponential generating function of Bernoulli numbers.
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Dedicated to the memory of Professor Jiarong YU
The author was supported by Labex CEMPI (Centre Europeen pour les Mathématiques, la Physique et leurs Interaction).
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Zhang, C. On Theta-Type Functions in the Form (x; q)∞. Acta Math Sci 41, 2086–2106 (2021). https://doi.org/10.1007/s10473-021-0617-z
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DOI: https://doi.org/10.1007/s10473-021-0617-z