A generalization of certain associated Bessel functions in connection with a group of shifts
Classical Analysis and ODEs
2023-06-22 v2
Abstract
Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions. We can consider this kernel as a special function. Some particular values of parameters involved in this special function are found to coincide with certain variants of Bessel functions. Using these connections, we also establish some analogues of orthogonality relations for Macdonald and Hankel functions.
Keywords
Cite
@article{arxiv.2204.00756,
title = {A generalization of certain associated Bessel functions in connection with a group of shifts},
author = {J. Choi and I. A. Shilin},
journal= {arXiv preprint arXiv:2204.00756},
year = {2023}
}