J. Choi ; I. A. Shilin - A generalization of certain associated Bessel functions in connection with a group of shifts

cm:9305 - Communications in Mathematics, May 12, 2022, Volume 30 (2022), Issue 1 - https://doi.org/10.46298/cm.9305
A generalization of certain associated Bessel functions in connection with a group of shiftsArticle

Authors: J. Choi ; I. A. Shilin

    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.


    Volume: Volume 30 (2022), Issue 1
    Published on: May 12, 2022
    Accepted on: April 6, 2022
    Submitted on: April 11, 2020
    Keywords: Mathematics - Classical Analysis and ODEs

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