The use of confluent hypergeometric functions in mathematical physics and the solution of an eigenvalue problem

Summary

Poiseuille flow in a cylindrical tube leads to eigenvalue problems connected with a special type of Whittaker functions, the eigenvalue ω occurring in the argument and the first index. In this paper an eigenvalue problem is solved by means of asymptotic expansion of the eigenvalue equation. The corresponding expansion of Whittaker's function for large ω, which is new, can be obtained in different ways, which are studied in detail. This paper is the first of a series on the same subject.