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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: We define a new difference equation analogue of the Bessel differential equation and investigate the properties of its solution, which we express using a $ {}_2F_1$ 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