Journal of Applied Mathematics and Stochastic Analysis 
Volume 8 (1995), Issue 4, Pages 415-421
doi:10.1155/S1048953395000384

Generalized Neumann and Kapteyn expansions

Harold Exton

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

Received 1 December 1994; Revised 1 June 1995

Abstract

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.