Analytic Continuation of Hypergeometric Functions in the Resonant Case
Classical Analysis and ODEs
2016-02-04 v1 High Energy Physics - Theory
Algebraic Geometry
Complex Variables
Abstract
We perform the analytic continuation of solutions to the hypergeometric differential equation of order to the third regular singularity, usually denoted , 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.
Cite
@article{arxiv.1602.01384,
title = {Analytic Continuation of Hypergeometric Functions in the Resonant Case},
author = {Emanuel Scheidegger},
journal= {arXiv preprint arXiv:1602.01384},
year = {2016}
}
Comments
32 pages