Geodesic
Integral relations for the Whittaker functions and the representations of the three-dimensional Lorentz group
Sbornik. Mathematics, Tome 10 (1970) no. 2, pp. 173-179 
N. Ya. Vilenkin; M. A. Shleinikova. Integral relations for the Whittaker functions and the representations of the three-dimensional Lorentz group. Sbornik. Mathematics, Tome 10 (1970) no. 2, pp. 173-179. http://geodesic.mathdoc.fr/item/SM_1970_10_2_a2/
@article{SM_1970_10_2_a2,
     author = {N. Ya. Vilenkin and M. A. Shleinikova},
     title = {Integral relations for the {Whittaker} functions and the representations of the three-dimensional {Lorentz} group},
     journal = {Sbornik. Mathematics},
     pages = {173--179},
     year = {1970},
     volume = {10},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_10_2_a2/}
}
TY  - JOUR
AU  - N. Ya. Vilenkin
AU  - M. A. Shleinikova
TI  - Integral relations for the Whittaker functions and the representations of the three-dimensional Lorentz group
JO  - Sbornik. Mathematics
PY  - 1970
SP  - 173
EP  - 179
VL  - 10
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1970_10_2_a2/
LA  - en
ID  - SM_1970_10_2_a2
ER  - 
%0 Journal Article
%A N. Ya. Vilenkin
%A M. A. Shleinikova
%T Integral relations for the Whittaker functions and the representations of the three-dimensional Lorentz group
%J Sbornik. Mathematics
%D 1970
%P 173-179
%V 10
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1970_10_2_a2/
%G en
%F SM_1970_10_2_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

We construct elements of the matrix which connects different bases for class I representations of the group $SO(2,1)$. These matrix elements are expressed in terms of Whittaker functions. In this way integral relations are obtained for these and orhte special functions. Bibliography: 5 titles.

[1] N. Ya. Vilenkin, Spetsialnye funktsii i teoriya predstavlenii grupp, Nauka, Moskva, 1965 | MR

[2] N. Ya. Vilenkin, “Kontinualnye teoremy slozheniya dlya gipergeometricheskoi funktsii”, Matem. cb., 65(107) (1964), 28–46 | MR | Zbl

[3] Akio Orihara, “On some integral formulas containing Bessel functions”, Publ. Research Inst. Math. Sciences, I (1965), 55–66 | MR

[4] Paul J. Sally, Jr., “Analytic continuation of the irreducible unitary representations of the universal covering group of $SL(2,R)$”, Memoirs Amer. Math. Soc., 1967, no. 69 | MR

[5] F. Oberhettinger, Tabellen zur Fourier transformation, Springer-Verlag, 1957 | MR | Zbl