The Wilson Function Transform

International Mathematics Research Notices

Volumn , Issue 52, 2003, Pages 2779-2817

  Groenevelt, Wolter ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0344253658     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s107379280313190x     Document Type: Article

References (23)

1. G. E. Andrews, R. Askey, and R. Roy, Special Functions, Encyclopedia of Mathematics and Its Applications, vol. 71, Cambridge University Press, Cambridge, 1999.
2. W. N. Bailey, Generalized Hypergeometric Series, Hafner Press, New York, 1972.
3. B. L. J. Braaksma and B. Meulenbeld, Integral transforms with generalized Legendre functions as kernels, Compositio Math. 18 (1967), 235-287.
4. A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions. Vols. I, II, McGraw-Hill, New York, 1953.
5. m,n(z), Indag Math. 27 (1965), 396-404 (German).
6. W. Groenevelt, E. Koelink, and H. Rosengren, Continuous Hahn functions as Clebsch-Gordan coefficients, to appear in Theory and Applications of Special Functions (M. E. H. Ismail and E. Koelink, eds.), Developments in Mathematics, Kluwer Academic Publishers. A Volume Dedicated to M. Rahman, http://arXiv.org/abs/math.CA/0302251.
7. M. E. H. Ismail, J. Letessier, G. Valent, and J. Wimp, Two families of associated Wilson polynomials, Canad. J. Math. 42 (1990), no. 4, 659-695.
8. R. Koekoek and R. F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Tech. Report 98-17, Department of Technical Mathematics and Informatics, Faculty of Information Technology and Systems, Delft University of Technology, Delft, 1998.
9. E. Koelink and J. V. Stokman, The Askey-Wilson function transform, Int. Math. Res. Not. 2001 (2001), no. 22, 1203-1227.
10. _, Fourier transforms on the quantum SU(1, 1) group, Publ. Res. Inst. Math. Sci. 37 (2001), no. 4, 621-715, with an appendix by M. Rahman.
11. T. H. Koornwinder, Jacobi functions and analysis on noncompact semisimple Lie groups, Special Functions: Group Theoretical Aspects and Applications (R. A. Askey, T. H. Koornwinder, and W. Schempp, eds.), Math. Appl., Reidel Publishing, Dordrecht, 1984, pp. 1-85.
12. _, Special orthogonal polynomial systems mapped onto each other by the Fourier-Jacobi transform, Orthogonal Polynomials and Applications (Bar-le-Duc, 1984) (C. Brezinski, A. Draux, A. P. Magnus, P. Maroni, and A. Ronveaux, eds.), Lecture Notes in Math., vol. 1171, Springer-Verlag, Berlin, 1985, pp. 174-183.
13. _, Group theoretic interpretations of Askey's scheme of hypergeometric orthogonal polynomials, Orthogonal Polynomials and Their Applications (Segovia, 1986) (M. Alfaro, J. S. Dehesa, F. J. Marcellán, J. L. Rubio de Francia, and J. Vinuesa, eds.), Lecture Notes in Math., vol. 1329, Springer-Verlag, Berlin, 1988, pp. 46-72.
14. D. R. Masson, Associated Wilson polynomials, Constr. Approx. 7 (1991), no. 4, 521-534.
15. Yu. A. Neretin, Beta integrals and finite orthogonal systems of Wilson polynomials, Mat. Sb. 193 (2002), no. 7, 131-148 (Russian).
16. F. W. J. Olver, Asymptotics and Special Functions, Computer Science and Applied Mathematics, Academic Press, New York, 1974.
17. S. N. M. Ruijsenaars, A generalized hypergeometric function satisfying four analytic difference equations of Askey-Wilson type, Comm. Math. Phys. 206 (1999), no. 3, 639-690.
18. 4 symmetry, to appear in Comm. Math. Phys.
19. _, A generalized hypergeometric function III. Associated Hilbert space transform, to appear in Comm. Math. Phys.
20. L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, 1966.
21. J. V. Stokman, An expansion formula for the Askey-Wilson function, J. Approx. Theory 114 (2002), no. 2, 308-342.
22. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis. An Introduction to the General Theory of Infinite Processes and of Analytic Functions: with an Account of the Principal Transcendental Functions, 4th ed., Cambridge University Press, New York, 1963.
23. J. A. Wilson, Some hypergeometric orthogonal polynomials, SIAM J. Math. Anal. 11 (1980), no. 4, 690-701.