共振情形下超几何函数的解析延拓
Analytic Continuation of Hypergeometric Functions in the Resonant Case
摘要：
利用Mellin-Barnes整表示的递推关系，将$n$阶超几何微分方程的解解析延拓到第三正则奇点，通常记为$z=1$.在共振情况下，必然存在对数解。我们将结果应用到Picard-Fuchs方程的某些单参数家庭的Calabi-Yau流形，被称为镜像四次和镜像五次。
英文摘要：
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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