Hermite-Weber and Airy Functions of Matrix Argument and their Holonomic Systems

Keimur H and Lia C

Published on: 2023-01-30

Abstract

We consider several special functions defined by matrix integrals on Hermitian matrix space. They are analogues of Gauss hypergeomeric, Kummer’s confluent hypergeometric, Bessel, Hermite-Weber and Airy functions. We give the systems of differential equations for these analogues of classical special functions and discuss their holonomicity and give their holonomic ranks.