Square Series Generating Function Transformations

9 Sep 2016

We construct new integral representations for transformations of the ordinary generating function for a sequence, $\langle f_n \rangle$, into the form of a generating function that enumerates the corresponding "square series" generating function for the sequence, $\langle q^{n^2} f_n \rangle$, at an initially fixed non-zero $q \in \mathbb{C}$. The new results proved in the article are given by integral-based transformations of ordinary generating function series expanded in terms of the Stirling numbers of the second kind... (read more)

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