Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 4, Pages 415-421

Generalized Neumann and Kapteyn expansions

Harold Exton

“Nyuggel”, Lunabister, Dunrossness, Shetland, ZE2 9JH, United Kingdom

Received 1 December 1994; Revised 1 June 1995

Copyright © 1995 Harold Exton. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Certain formal series of a most general nature are specialized so as to deduce expansions in terms of a class of generalized hypergeometric functions. These series generalize the Neumann and Kapteyn series in the theory of Bessel functions, and their convergence is investigated. An example of a succinct expansion is also given.