Modified q-Bessel functions and q-Macdonald functions

Sbornik Mathematics

Volumn 187, Issue 9-10, 1996, Pages 1525-1544

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

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030300532     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/sm1996v187n10abeh000167     Document Type: Article

References (18)

1. F. H. Jackson, "The application of basic numbers to Bessel's and Legendre's functions", Proc. London Math. Soc. (2). 2 (1905), 192-220.
2. R. Floreanini and L. Vinet, "Addition formulas for q-Bessel functions", Preprint, University of Montreal, UdeM-LPN-TH60, 1991; "Representations of quantum algebras and q-special functions", Preprint, Université de Montreal, 1991.
3. R. Floreanini and L. Vinet, "Addition formulas for q-Bessel functions", Preprint, University of Montreal, UdeM-LPN-TH60, 1991; "Representations of quantum algebras and q-special functions", Preprint, Université de Montreal, 1991.
4. L. Vaksman and L. Korogodskiǐ, "The algebra of bounded functions of the quantum group of 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).
5. L. Vaksman and L. Korogodskiǐ, "The algebra of bounded functions of the quantum group of 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).
6. N. Ya. Vilenkin, Special functions and the theory of group representations, 2nd ed., Nauka, Moscow 1991; English transl. of 1st ed., Amer. Math. Soc., Providence, RI 1968.
7. N. Ya. Vilenkin, Special functions and the theory of group representations, 2nd ed., Nauka, Moscow 1991; English transl. of 1st ed., Amer. Math. Soc., Providence, RI 1968.
8. E. B. Dynkin, "Non-negative eigenfunctions of the Laplace-Beltrami operator and Brownian motion in certain symmetric spaces", Dokl. Akad. Nauk SSSR 141 (1961), 288-291; English transl. in Soviet Math. Dokl. 2 (1961).
9. E. B. Dynkin, "Non-negative eigenfunctions of the Laplace-Beltrami operator and Brownian motion in certain symmetric spaces", Dokl. Akad. Nauk SSSR 141 (1961), 288-291; English transl. in Soviet Math. Dokl. 2 (1961).
10. M. Olshanetsky [Ol'shanetskiǐ], "Martin boundaries for real semisimple Lie groups", J. Funct. Anal. 126 (1994), 169-216.
11. H. P. B. Jacquet, "Fonctions de Whittaker associées aux groupes de Chevalley", Bull. Soc. Math. France 95 (1967), 243-309.
12. G. Schiffmann, "Intégrales d'entrelacement et fonctions de Whittaker", Bull. Soc. Math. France. 99 (1971), 3-72.
13. M. A. Semenov-Tian-Shansky, Quantization of open Toda lattices, Itogi Nauki i Tekhniki: Sovrem. Probl. Mat.: Fund. Naprav., vol. 16, VINITI, Moscow 1987, pp. 194-226; English transl. in [Dynamical Systems, VII], Encyclopaedia of Math. Sciences, vol. 16, Springer-Verlag, Berlin 1994.
14. M. A. Semenov-Tian-Shansky, Quantization of open Toda lattices, Itogi Nauki i Tekhniki: Sovrem. Probl. Mat.: Fund. Naprav., vol. 16, VINITI, Moscow 1987, pp. 194-226; English transl. in [Dynamical Systems, VII], Encyclopaedia of Math. Sciences, vol. 16, Springer-Verlag, Berlin 1994.
15. P. Ginsparg and G. Moore, Lectures on 2d gravity and 2d strings, Preprint, Yale Univ. TCTP-P23-92.
16. M. Ol'shanetskiǐ and V. Rogov, "Liouville quantum mechanics on a lattice from geometry of quantum Lorentz group", J. Phys. A. 27 (1994), 4669-4683.
17. G. Gasper and M. Rahman, Basic hypergeometric series, Cambridge Univ. Press, Cambridge 1990.
18. A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher transcendental functions, vol. 2 (based, in part, on notes left by Harry Bateman), McGraw-Hill, New York 1953.