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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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.
- M. Abdalla, On the incomplete hypergeometric matrix functions, Ramanujan J. 43 (2017), no. 3, 663–678. MR 3670287, DOI 10.1007/s11139-016-9795-z
- Mohamed Abdalla, Special matrix functions: characteristics, achievements and future directions, Linear Multilinear Algebra 68 (2020), no. 1, 1–28. MR 4037069, DOI 10.1080/03081087.2018.1497585
- Ahmed Bakhet, Yong Jiao, and Fuli He, On the Wright hypergeometric matrix functions and their fractional calculus, Integral Transforms Spec. Funct. 30 (2019), no. 2, 138–156. MR 3881345, DOI 10.1080/10652469.2018.1543669
- C. Calderón, Y. González, I. Pacharoni, S. Simondi, and I. Zurrián, $2\times 2$ hypergeometric operators with diagonal eigenvalues, J. Approx. Theory 248 (2019), 105299, 17. MR 4013141, DOI 10.1016/j.jat.2019.105299
- Emilio Defez and Lucas Jódar, Chebyshev matrix polynomials and second order matrix differential equations, Util. Math. 61 (2002), 107–123. MR 1899321
- Ravi Dwivedi and Vivek Sahai, On the hypergeometric matrix functions of several variables, J. Math. Phys. 59 (2018), no. 2, 023505, 15. MR 3763251, DOI 10.1063/1.5019334
- L. Jódar and J. C. Cortés, On the hypergeometric matrix function, Proceedings of the VIIIth Symposium on Orthogonal Polynomials and Their Applications (Seville, 1997), 1998, pp. 205–217. MR 1662696, DOI 10.1016/S0377-0427(98)00158-7
- Robb J. Muirhead, Expressions for some hypergeometric functions of matrix argument with applications, J. Multivariate Anal. 5 (1975), no. 3, 283–293. MR 381137, DOI 10.1016/0047-259X(75)90046-9
- D. K. Nagar and S. Nadarajah, Appell’s hypergeometric functions of matrix arguments, Integral Transforms Spec. Funct. 28 (2017), no. 2, 91–112. MR 3574323, DOI 10.1080/10652469.2016.1252762
- Xiao-Jun Yang, An introduction to hypergeometric, supertrigonometric, and superhyperbolic functions, Elsevier/Academic Press, London, [2021] ©2021. MR 4251072
- P. V. Pikhitsa and U. R. Fischer, Exact surface-wave spectrum of a dilute quantum liquid, Phys. Rev. B 99 (2019), 184504.
- P. Román and S. Simondi, The generalized matrix valued hypergeometric equation, Internat. J. Math. 21 (2010), no. 2, 145–155. MR 2650365, DOI 10.1142/S0129167X10005970
- Ayman Shehata, Some relations on Konhauser matrix polynomials, Miskolc Math. Notes 17 (2016), no. 1, 605–633. MR 3527907, DOI 10.18514/MMN.2016.1126
- Juan A. Tirao, The matrix-valued hypergeometric equation, Proc. Natl. Acad. Sci. USA 100 (2003), no. 14, 8138–8141. MR 1989346, DOI 10.1073/pnas.1337650100
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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
