Discrete Matrix Hypergeometric Functions

Author

Tom Cuchta
David E. Grow, Missouri University of Science and TechnologyFollow
Nick Wintz

Abstract

We generalize the scalar discrete hypergeometric series to allow for matrix parameters. We show their connection to classical matrix hypergeometric series, derive conditions for convergence on the boundary disk, show criteria for divergence, derive integral representations, and establish some difference equations they solve. We also highlight the special case of discrete matrix Bessel functions, whose scalar analogue has proved useful in applications.

Recommended Citation

T. Cuchta et al., "Discrete Matrix Hypergeometric Functions," Journal of Mathematical Analysis and Applications, vol. 518, no. 2, article no. 126716, Elsevier, Feb 2023.

The definitive version is available at https://doi.org/10.1016/j.jmaa.2022.126716

Department(s)

Mathematics and Statistics

Keywords and Phrases

Convergence; Difference Equation; Divergence; Hypergeometric Series; Matrix Analysis; Matrix Special Functions

International Standard Serial Number (ISSN)

1096-0813; 0022-247X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 Elsevier, All rights reserved.

Publication Date

15 Feb 2023