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