Extended Hurwitz results for hypergeometric functions arising in spectral theory

Authors:
B. M. Brown;M. S. P. Eastham
Affiliations:
Department of Computer Science, University of Cardiff, Newport Road, P.O. Box 926, Cardiff CF24 3XF, UK;Department of Computer Science, University of Cardiff, Newport Road, P.O. Box 926, Cardiff CF24 3XF, UK
Venue:
Journal of Computational and Applied Mathematics - Special issue: On the occasion of the eightieth birthday of prof. W.M. Everitt
Year:
2004

Citing 1
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Abstract

A result of Hurwitz is that the Bessel function J-v(c)(v 0,c 0) has no zeros for 2N v N + 1 with integer N. Here corresponding results for hypergeometric and confluent hypergeometric functions are given. Extensions are obtained where the power series are terminated after 2N + 1 terms and larger zero-free intervals (2N,V) are found.