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Divergence criteria for matrix generalized hypergeometric series


Authors: Tom Cuchta, David Grow and Nick Wintz
Journal: Proc. Amer. Math. Soc. 150 (2022), 1235-1240
MSC (2020): Primary 33C20; Secondary 15A16, 40A05
DOI: https://doi.org/10.1090/proc/15773
Published electronically: November 30, 2021
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Abstract: We provide proofs of sharp divergence criteria for a large class of matrix hypergeometric series by estimating lower norm bounds of their terms. Difficulties in extending our techniques to singular matrix parameters are illustrated.


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Additional Information

Tom Cuchta
Affiliation: Department of Computer Science and Mathematics, Fairmont State University, Fairmont, West Virginia 26554
MR Author ID: 863360
ORCID: 0000-0002-6827-4396
Email: tcuchta@fairmontstate.edu

David Grow
Affiliation: Department of Mathematics & Statistics, Missouri University of Science & Technology, Rolla, Missouri 65409
MR Author ID: 213200
Email: grow@mst.edu

Nick Wintz
Affiliation: Department of Mathematics, Computer Science, and Information Technology, Lindenwood University, St. Charles, Missouri 63301
MR Author ID: 767100
Email: nwintz@lindenwood.edu

Keywords: Special functions, matrix hypergeometric, lower bound, divergence
Received by editor(s): March 18, 2021
Received by editor(s) in revised form: June 18, 2021
Published electronically: November 30, 2021
Communicated by: Mourad Ismail
Article copyright: © Copyright 2021 American Mathematical Society