# Certain relations between Bessel and Whittaker functions related to some diagonal and block-diagonal $3\times 3$-matrices

Volume 10, Issue 2, pp 560--574
Publication Date: February 20, 2017 Submission Date: September 02, 2016
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### Authors

I. A. Shilin - Department of Mathematics, Sholokhov Moscow State University for the Humanities, Verhnya Radishevskaya 16-18, Moscow 109240, Russia. - Department of Energetics, University of Economics and Energetics, Kirovogradskaya ul. 11-1, 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 block-diagonal 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.

•  33C10
•  33C80
•  33B15
•  33C05

### References

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