%0 Journal Article
%T Certain relations between Bessel and Whittaker functions related to some diagonal and block-diagonal \(3\times 3\)-matrices
%A Shilin, I. A.
%A Choi, J.
%J Journal of Nonlinear Sciences and Applications
%D 2017
%V 10
%N 2
%@ ISSN 2008-1901
%F Shilin2017
%X 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.
%9 journal article
%R 10.22436/jnsa.010.02.20
%U http://dx.doi.org/10.22436/jnsa.010.02.20
%P 560--574
%0 Book
%T Table of Integrals, Series, and Products
%A I. S. Gradshteyn
%A I. M. Ryzhik
%D 2007
%I Translated from the Russian. Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger., Academic Press
%C Amsterdam
%F Gradshteyn2007
%0 Book
%T Integrals and Series, Vol. 1: Elementary Functions
%A A. P. Prudnikov
%A Yu. A. Brychkov
%A O. I. Marichev
%D 1986
%I OPA (Overseas Publishers Association), Amsterdam B. V. Published under the license of Gordon and Breach Science Publishers
%C New York
%F Prudnikov1986
%0 Journal Article
%T Double SO(2, 1)-integrals and formulas for Whittaker functions
%A I. A. Shilin
%J Russian Math.
%D 2012
%V 56
%F Shilin2012
%0 Journal Article
%T Certain connections between the spherical and hyperbolic bases on the cone and formulas for related special functions
%A I. A. Shilin
%A J. S. Choi
%J Integral Transforms Spec. Funct.
%D 2014
%V 25
%F Shilin2014
%0 Journal Article
%T Some connections between the spherical and parabolic bases on the cone expressed in terms of the Macdonald function
%A I. A. Shilin
%A J. Choi
%J Abstr. Appl. Anal.
%D 2014
%V 2014
%F Shilin2014
%0 Journal Article
%T Transformations of bases related to the six-dimensional split orthogonal group and special functions
%A I. A. Shilin
%A J. Choi
%J
%D submitted
%V
%F Shilinsubmitted
%0 Book
%T Zeta and q-Zeta Functions and Associated Series and Integrals
%A H. M. Srivastava
%A J. Choi
%D 2012
%I Elsevier Science Publishers
%C Amsterdam
%F Srivastava2012
%0 Journal Article
%T Integral relations for the Whittakers functions and the representations of the threedimensional Lorentz group
%A N. J. Vilenkin
%A M. A. Sleinikova
%J Math. USSR Sb.
%D 1970
%V 10
%F Vilenkin1970