The Bessel difference equation

Authors:
Martin Bohner and Tom Cuchta

Journal:
Proc. Amer. Math. Soc. **145** (2017), 1567-1580

MSC (2010):
Primary 33C05, 39A12, 39A10; Secondary 39A21

DOI:
https://doi.org/10.1090/proc/13416

Published electronically:
December 30, 2016

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Abstract | References | Similar Articles | Additional Information

Abstract: We define a new difference equation analogue of the Bessel differential equation and investigate the properties of its solution, which we express using a hypergeometric function. We find analogous formulas for Bessel function recurrence relations, a summation transformation which is identical to the Laplace transform of classical Bessel functions, and oscillation.

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Additional Information

**Martin Bohner**

Affiliation:
Department of Mathematics and Statistics, Missouri University of Science and Technology, 400 W. 12th Street, Rolla, Missouri 65409-0020

Email:
bohner@mst.edu

**Tom Cuchta**

Affiliation:
Department of Mathematics and Statistics, Missouri University of Science and Technology, 400 W. 12th Street, Rolla, Missouri 65409-0020

Email:
tcvh5@mst.edu

DOI:
https://doi.org/10.1090/proc/13416

Keywords:
Discrete Bessel functions,
discrete oscillation,
delay difference equations,
hypergeometric series,
contiguous relation

Received by editor(s):
March 14, 2016

Received by editor(s) in revised form:
April 27, 2016

Published electronically:
December 30, 2016

Communicated by:
Mourad Ismail

Article copyright:
© Copyright 2016
American Mathematical Society