Discrete Matrix Hypergeometric Functions

Tom Cuchta; David E. Grow; Nick Wintz

doi:10.1016/j.jmaa.2022.126716

Discrete Matrix Hypergeometric Functions

Tom Cuchta
, David E. Grow
, Nick Wintz

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	Journal of Mathematical Analysis and Applications
Volume	518
DOIs	https://doi.org/10.1016/j.jmaa.2022.126716
State	Published - Feb 15 2023

Keywords

Convergence
Difference Equation
Divergence
Hypergeometric Series
Matrix Analysis
Matrix Special Functions

Disciplines

Statistics and Probability

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10.1016/j.jmaa.2022.126716License: Unspecified

https://doi.org/10.1016/j.jmaa.2022.126716

Cite this

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title = "Discrete Matrix Hypergeometric Functions",

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.",

keywords = "Convergence, Difference Equation, Divergence, Hypergeometric Series, Matrix Analysis, Matrix Special Functions",

author = "Tom Cuchta and Grow, \{David E.\} and Nick Wintz",

year = "2023",

month = feb,

day = "15",

doi = "10.1016/j.jmaa.2022.126716",

language = "American English",

volume = "518",

journal = "Journal of Mathematical Analysis and Applications",

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T1 - Discrete Matrix Hypergeometric Functions

AU - Cuchta, Tom

AU - Grow, David E.

AU - Wintz, Nick

PY - 2023/2/15

Y1 - 2023/2/15

N2 - 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.

AB - 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.

KW - Convergence

KW - Difference Equation

KW - Divergence

KW - Hypergeometric Series

KW - Matrix Analysis

KW - Matrix Special Functions

UR - https://scholarsmine.mst.edu/math_stat_facwork/1153

UR - https://doi.org/10.1016/j.jmaa.2022.126716

U2 - 10.1016/j.jmaa.2022.126716

DO - 10.1016/j.jmaa.2022.126716

M3 - Article

SN - 1096-0813

VL - 518

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

ER -

Discrete Matrix Hypergeometric Functions

Abstract

Keywords

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