Integral Transforms and Special Functions ( IF 0.7 ) Pub Date : 2021-05-19 , DOI: 10.1080/10652469.2021.1929206 S. I. Bezrodnykh 1, 2
We consider the Lauricella hypergeometric function , depending on variables , and obtain formulas for its analytic continuation into the vicinity of a singular set which is an intersection of the hyperplanes . It is assumed that all N variables are large in modulo. This formulas represent the function outside of the unit polydisk in the form of linear combinations of other N-multiple hypergeometric series that are solutions of the same system of partial differential equations as . The derived hypergeometric series are N-dimensional analogues of the Kummer solutions that are well known in the theory of the classical hypergeometric Gauss equation.
中文翻译:
Lauricella 函数 FD(N) 的解析延展,用于超平面 {zj = zl} 附近的大模变量
我们考虑 Lauricella 超几何函数, 根据变量, 并获得其解析延拓到作为超平面交集的奇异集附近的公式. 假设所有N个变量在模上都很大。此公式表示函数以其他N多超几何级数的线性组合形式存在于单位 polydisk 之外,这些超几何级数是相同的偏微分方程组的解. 导出的超几何级数是经典超几何高斯方程理论中众所周知的 Kummer 解的N维类似物。