Abstract

In investigation of boundary-value problems for certain partial differential equations arising in applied mathematics, we often need to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find explicit linearly independent solutions for the system. In this investigation, we construct special solutions for a certain class of degenerating differential equations of parabolic type of a high order. These special solutions are expressed in terms of hypergeometric functions of one variable.

中文翻译：

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三阶退化模型抛物方程解的超几何展开

摘要

在研究应用数学中某些偏微分方程的边值问题时，我们经常需要研究超几何函数满足的偏微分方程系统的解，并找到该系统的显式线性独立解。在这项研究中，我们为一类退化的高阶抛物型微分方程构造了特殊的解。这些特殊解以一个变量的超几何函数表示。