Quadratic q-exponentials and connection coefficient problems

Proceedings of the American Mathematical Society

Volumn 127, Issue 10, 1999, Pages 2931-2941

  Ismail, Mourad E H ^a   Rahman, Mizan ^b   Stanton, Dennis ^c  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

^b CARLETON UNIVERSITY   (Canada)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Askey wilson polynomials; Continuous q ultraspherical polynomials; Q bessel functions; Q exponential functions

Indexed keywords

EID: 22844455171     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-99-05017-0     Document Type: Article

References (19)

1. [Al:Ch] W. A. Al-Salam and T. S. Chihara, Convolutions of orthogonal polynomials, SIAM J. Math. Anal. 7 (1976), 16-28. MR 53:3381
2. [An] G. E. Andrews, Connection coefficient problems and partitions, Proc. Symp. Pure Math 34 (1979), 1-24. MR 80c:33004
3. [As:Is] R. A. Askey and M. E. H. Ismail, A generalization of ultraspherical polynomials, Studies in Pure Mathematics (P. Erdös, ed.), Birkhauser, Basel, 1983, pp. 55-78. MR 87a:33015
4. [As:Is2] R. A. Askey and M. E. H. Ismail, Recurrence relations, continued fractions and orthogonal polynomials, Memoirs Amer. Math. Soc. 49 (1984). MR 85g:33008
5. [As:Wi] R. A. Askey and J. A. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Memoirs Amer. Math. Soc. 54 (1985). MR 87a:05023
6. [At:Su] N. M. Atakishiev and S. K. Suslov, Difference hypergeometric functions, Progress in Approximation Theory, An International Perspective (A. A. Gonchar and E. B. Saff, ed.), Springer-Verlag, New York, 1992, pp. 1-35. MR 94k:33039
7. [Fi:Is] J. Fields and M. E. H. Ismail, Polynomial expansions, Mathematics of Computation 29 (1975), 894-902. MR 51:8680
8. [Fl:Vi] R. Florcanini and L. Vinet, A model for the continuous q-ultraspherical polynomials, 3. Math. Phys. 36 (1995), 3800-3813. MR 96d:33012
9. [Fl:Le:Vi] R. Floreanini, J. LeTourneux and L. Vinet, More on the q-oscillator algebra and q-orthogonal polynomials, Journal of Physics A 28 (1995), L287-L293. MR 96e:33043
10. [Fl:Le:Vi2] R. Floreanini, J. LeTourneux and L. Vinet, Symmetry techniques for the Al-Salam-Chihara polynomials, J. Phys. A 30 (1997), 3107-3114. MR 98k:33036
11. [Ga:Ra] G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990. MR 91d:33034
12. [Ge:St] I. Gessel and D. Stanton, Applications ofq-Lagrange inversion to basic hypergeometric series, Trans. Amer. Math. Soc. 277 (1983), 173-201. MR 84f:33009
13. v+ax (x) and the associated orthogonal polynomials, J. Math. Anal. Appl. 86 (1982), 1-19. MR 83c:33010
14. [Is:Ma:Su] M. E. H. Ismail, D. Masson and S. Suslov, The q-Bessel functions on q-quadratic grid (to appear).
15. [Is:Ra:Zh] M. E. H. Ismail, M. Rahman and R. Zhang, Diagonalization of certain integral operators II, J. Comp. Appl. Math. 68 (1996), 163-196. MR 98d:33011
16. [Is:Zh] M. E. H. Ismail and R. Zhang, Diagonalization of certain integral operators, Advances in Math. 109 (1994), 1-33. MR 96d:39005
17. [Lu] Y. Luke, The Special Functions and Their Approximations, volume 2, Academic Press, New York, 1969. MR 40:2909
18. [Ra] M. Rahman, An integral representation and some transformation properties of q-Bessel functions, 3. Math. Anal. Appl. 125 (1987), 58-71. MR 88h:33020
19. [Su] S. K. Suslov, Addition theorems for some q-exponential and trigonometric functions, Methods and Applications of Analysis 4 (1997), 11-32. CMP 97:14