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.
Changgui ZHANG
. ON THETA-TYPE FUNCTIONS IN THE FORM (x;q)∞[J]. Acta mathematica scientia, Series B, 2021
, 41(6)
: 2086
-2106
.
DOI: 10.1007/s10473-021-0617-z
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