ON THETA-TYPE FUNCTIONS IN THE FORM (x;q)∞

doi:10.1007/s10473-021-0617-z

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (6): 2086-2106.doi: 10.1007/s10473-021-0617-z

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ON THETA-TYPE FUNCTIONS IN THE FORM (x;q)_∞

Changgui ZHANG

Laboratoire P. Painlevé(UMR-CNRS 8524), Département de mathématiques, FST, Université de Lille, Cité scientifique, 59655 Villeneuve d'Ascq cedex, France

Received:2021-05-06 Revised:2021-08-11 Online:2021-12-25 Published:2021-12-27
Supported by:
The author was supported by Labex CEMPI (Centre Européen pour les Mathémmatiques, la Physique et leurs Interaction).

Abstract

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.

Key words: q-series, Mock theta-functions, Stokes phenomenon, continued fractions

CLC Number:

34M30

Changgui ZHANG. ON THETA-TYPE FUNCTIONS IN THE FORM (x;q)_∞[J].Acta mathematica scientia,Series B, 2021, 41(6): 2086-2106.

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References 15

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ON THETA-TYPE FUNCTIONS IN THE FORM (x;q)_∞

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