Analytic Continuation of Hypergeometric Functions in the Resonant Case

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.

32 pages

References in corpus (1)

• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds

Cited by in corpus (4)

• Quantum periods of Calabi-Yau fourfolds
• Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring
• Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
• A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds