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Commun. Korean Math. Soc. 2017; 32(4): 999-1008
Online first article October 12, 2017 Printed October 31, 2017
https://doi.org/10.4134/CKMS.c170027
Copyright © The Korean Mathematical Society.
A family of series and integrals involving Whittaker, Bessel functions, and their products derivable from the representation of the group $SO(2,1)$
Junesang Choi, I. A. Shilin
Dongguk University, Moscow State Pedagogical University
By mainly using certain properties arising from the semisimple Lie group $SO(2,1)$, we aim to show how a family of some interesting formulas for bilateral series and integrals involving Whittaker, Bessel functions, and their product can be obtained.
Keywords: Whittaker function, Bessel functions, Macdonald function, semisimple Lie group $SO(2,1)$, Cartan decomposition, matrix elements of representation
MSC numbers: Primary 33C10, 33C80; Secondary 33B15, 33C05
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