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The family of the Taylor series f_{\epsilon}(z)=\sum\limits_{0\leq{}n<\infty}e^{-\epsilon n^2}z^n is considered, where theparameter \epsilon, which enumerates the family, runs over ]0,\infty[. Thelimiting behavior of this family is studied as \epsilon\to+0.

On summation of the Taylor series of the function 1/(1-z) by the theta summation method