Certain relations between Bessel and Whittaker functions related to some diagonal and blockdiagonal \(3\times 3\)matrices
Authors
I. A. Shilin
 Department of Mathematics, Sholokhov Moscow State University for the Humanities, Verhnya Radishevskaya 1618, Moscow 109240, Russia.
 Department of Energetics, University of Economics and Energetics, Kirovogradskaya ul. 111, Moscow 117587, Russia.
J. Choi
 Department of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea.
Abstract
The authors derive the matrix elements of the linear operators which appear under the representation of the group SO(2, 1)
and correspond to some diagonal or blockdiagonal matrices belonging to the above group. Then, by applying these matrix
elements, that is, from a group theoretical point of view, the authors show how certain interesting integral and series representations
of the Whittaker function of the second kind and some formulas for the (basic and modified) Bessel functions can be
obtained. A special case of one of the results presented here is indicated to be also a special one of a known formula.
Keywords
 Whittaker function
 Bessel functions
 Macdonald function
 semisimple Lie group SO(2، 1)
 matrix elements of representation.
 Whittaker function
 Bessel functions
 Macdonald function
 semisimple Lie group SO(2، 1)
 matrix elements of representation.
MSC
References

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