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arXiv · 1602.01384

Analytic Continuation of Hypergeometric Functions in the Resonant Case

Emanuel Scheidegger
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Abstract

We perform the analytic continuation of solutions to the hypergeometric differential equation of order $n$ to the third regular singularity, usually denoted $z=1$, with the help of recurrences of their Mellin--Barnes integral representations. In the resonant case, there are necessarily logarithmic solutions. We apply the result to Picard-Fuchs equations of certain one--parameter families of Calabi--Yau manifolds, known as the mirror quartic and the mirror quintic.

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Emanuel Scheidegger. 2016-02-03. Analytic Continuation of Hypergeometric Functions in the Resonant Case. https://arxiv.org/abs/1602.01384

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