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arXiv · 1608.07147

On functions K and E generated by a sequence of moments

Avner Kiro·Mikhail Sodin
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Abstract

We study the asymptotic behaviour of the entire function \[ E(z) = \sum_{n\ge 0} \frac{z^n}{\gamma (n+1)} \] and the analytic function \[ K(z) = \frac1{2\pi {\rm i}}\, \int_{c-{\rm i}\infty}^{c+{\rm i}\infty} z^{-s}\gamma (s)\, {\rm d}s\,, \] which naturally appear in various classical problems of analysis.

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Avner Kiro, Mikhail Sodin. 2016-08-25. On functions K and E generated by a sequence of moments. https://arxiv.org/abs/1608.07147

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