q-integral representations of modified q-Bessel functions and q-Macdonald functions

Sbornik Mathematics

Volumn 188, Issue 7-8, 1997, Pages 1235-1258

  Ol'shanetskii M A ^a,b   Rogov, V B K ^a,b  

^a INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

^b RUSSIAN UNIVERSITY OF TRANSPORT   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031286456     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/sm1997v188n08abeh000248     Document Type: Article

References (15)

1. M. A. Ol'shanetskiǐ and V.-B. K. Rogov, "Modified q-Bessel functions and q-Macdonald functions", Mat. Sb. 187:10 (1996), 109-128; English transl. in Sbornik: Math. 188:9-10 (1996).
2. M. A. Ol'shanetskiǐ and V.-B. K. Rogov, "Modified q-Bessel functions and q-Macdonald functions", Mat. Sb. 187:10 (1996), 109-128; English transl. in Sbornik: Math. 188:9-10 (1996).
3. F. H. Jackson, "The application of basic numbers to Bessel's and Legendre's functions", Proc. London Math. Soc. (2). 2 (1905), 192-220.
4. N. Ya. Vilenkin, Special functions and the theory of group representations, 2nd ed., Nauka, Moscow 1991; English transl. of the 1st ed., Amer. Math. Soc., Providence, RI 1968.
5. N. Ya. Vilenkin, Special functions and the theory of group representations, 2nd ed., Nauka, Moscow 1991; English transl. of the 1st ed., Amer. Math. Soc., Providence, RI 1968.
6. L. L. Vaksman and L. I. Korogodskiǐ, "The algebra of bounded functions of the quantum group of the motions of the plane and q-analogs of Bessel functions", Dokl. Akad. Nauk SSSR 304 (1989), 1036-1040; English transl. in Soviet Math. Dokl. 39 (1989).
7. L. L. Vaksman and L. I. Korogodskiǐ, "The algebra of bounded functions of the quantum group of the motions of the plane and q-analogs of Bessel functions", Dokl. Akad. Nauk SSSR 304 (1989), 1036-1040; English transl. in Soviet Math. Dokl. 39 (1989).
8. R. Floreanini and L. Vinet, "Addition formulas for q-Bessel functions", J. Math. Phys. 33 (1992), 2984-2988.
9. H. T. Koelink, "The quantum group of plane motions and the Hahn-Exton q-Bessel function", Duke Math. J. 76 (1994), 483-508.
10. H. P. B. Jacquet, "Fonctions de Whittaker associées aux groupes de Chevalley", Bull. Soc. Math. France 95 (1967), 243-309.
11. M. Hashizume, "Whittaker functions on semisimple Lie groups", Hiroshima Math. J. 12 (1982), 259-293.
12. M. Olshanetsky [Ol'shanetskiǐ] and V. Rogov, "Liouville quantum mechanics on a lattice from the geometry of the quantum Lorentz group", J. Phys. A: Math. Gen. 27 (1994), 4669-4683.
13. G. Gasper and M. Rahman, Basic hypergeometric series, Cambridge University Press, Cambridge 1990.
14. A. P. Prudnikov, Yu. A Brychkov, and O. I Marychev, Integrals and series, vol. 1, Nauka, Moscow 1986; English transl., Gordon and Breach, New York 1988.
15. A. Erdélyi, W. Magnus, F. Oberhettiger, and F. G. Tricomi, Higher transcendental functions, vol. 2; (based, in part, on notes left by Harry Bateman), McGraw-Hill, New York 1953.