标题： 拉普拉斯方程在汉克尔积分路径外部以及超几何函数的新恒等式 显示英文标题

标题： The Laplace equation for the exterior of the Hankel contour and novel identities for hypergeometric functions

摘要： 通过使用共形映射，可以将某些拉普拉斯方程边界值问题的解用包含给定边界数据的单个积分来表示。 我们表明，这样的显式公式可用于获得特殊函数的新恒等式。 一种方便的工具是所谓的\emph{全局关系}，它最近出现在一系列边界值问题中。 作为具体应用，我们分析了在所谓的 Hankel 轨道外部的拉普拉斯方程的 Neumann 边界值问题，该轨道出现在伽马函数和黎曼 zeta 函数的定义中。 通过利用该问题的显式解，我们推导出大量涉及超几何函数的新恒等式。 显示英文摘要

摘要： By employing conformal mappings, it is possible to express the solution of certain boundary value problems for the Laplace equation in terms of a single integral involving the given boundary data. We show that such explicit formulae can be used to obtain novel identities for special functions. A convenient tool for deriving this type of identities is the so-called \emph{global relation}, which has appeared recently in a wide range of boundary value problems. As a concrete application, we analyze the Neumann boundary value problem for the Laplace equation in the exterior of the so-called Hankel contour, which is the contour that appears in the definition of both the gamma and the Riemann zeta functions. By utilizing the explicit solution of this problem, we derive a plethora of novel identities involving the hypergeometric function.