Some orthogonal very-well-poised 8φ7-functions that generalize Askey-Wilson polynomials

Ramanujan Journal

Volumn 5, Issue 2, 2001, Pages 183-218

  Suslov, Sergei K ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Askey Wilson polynomials; Basic hypergeometric series; Orthogonal functions; q Bessel functions

Indexed keywords

EID: 0035539589     PISSN: 13824090     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011439924912     Document Type: Article

References (39)

1. G.E. Andrews and R. A. Askey, "Classical orthogonal polynomials," in Polynômes orthogonaux et applications, vol. 1171, Springer-Verlag, 1985, pp. 36-62. Lecture Notes in Math.
2. R.A. Askey, "Difference operators and orthogonal polynomials," Rendiconti di Matematica, series VII, 14 (1994), 135-144.
3. R.A. Askey, Private communication.
4. R. A. Askey. M. Rahman, and S.K. Suslov, "On a general q-Fourier transformation with nonsymmetric kernels," J. Comp. Appl. Math. 68 (1996), 25-55.
5. R.A. Askey and J.A. Wilson, "A set of orthogonal polynomials that generalize Racah coefficients or 6j-symbols," SIAM J. Math. Anal. 10 (1979), 1008-1016.
6. R.A. Askey and J.A. Wilson. "Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials," Memoirs Amer. Math. Soc. Number 319 (1985).
7. N.M. Atakishiyev, M. Rahman, and S.K. Suslov, "On the classical orthogonal polynomials," Constr. Approx. 11 (1995). 181-226.
8. N.M. Atakishiyev and S.K. Suslov, "Difference hypergeometric functions," in Progress in Approximation Theory: An International Perspective, Vol. 19: Springer Series in Computational Mathematics (A.A. Gonchar and E.B. Saff, eds.), Springer-Verlag, 1992, pp. 1-35.
9. N.M. Atakishiyev and S.K. Suslov, "On the Askey-Wilson polynomials," Constr. Approx. 8 (1992). 363-369.
10. B.M. Brown, W.D. Evans, and M.E.H. Ismail, "The Askey-Wilson polynomials and q-Sturm-Liouville problems," Math. Proc. Cambridge Philos. Soc. 119 (1996), 1-16.
11. J. Bustoz and S.K. Suslov, "Basic analog of Fourier series on a q-quadratic grid," Methods and Applications of Analysis 5 (1998), 1-38.
12. G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990.
13. R.W. Gosper, Jr. and S.K. Suslov, "Numerical investigation of basic Fourier series," in q-Series from a Contemporary Perspective, Vol. 254: Contemporary Mathematics (M.E.H. Ismail and D.R. Stanton, eds.). American Mathematical Society, 2000, pp. 199-227.
14. F.A. Grünbaum and L. Haine, "On q-analogue of Gauss equation and some q-Riccati equations," in Special Functions, q-Series and Related Topics. Vol. 14: Fields Institute Communications (M.E.H. Ismail, D.R Masson, and M. Rahman, eds.). American Mathematical Society, 1997, pp. 77-81.
15. M.E.H. Ismail, Some properties of Jackson's third q-Bessel function, to appear.
16. M.E.H. Ismail, D.R. Masson, and S.K. Suslov, "Some generating functions for q-polynomials," in Special Functions. q-Series and Related Topics, Vol. 14: Fields Institute Communications (M.E.H. Ismail, D.R. Masson, and M. Rahman, eds.), American Mathematical Society, 1997, pp. 91-108.
17. M.E.H. Ismail, D.R. Masson, and S.K. Suslov, "The q-Bessel functions on a q-quadratic grid," in Algebraic Methods and q-Special Functions, Vol. 22: CRM Proceedings & Lecture Notes (J.F. van Diejen and L. Vinet, eds.), American Mathematical Society, 1999, pp. 183-200.
18. M.E.H. Ismail, D.R. Masson, and S.K. Suslov, Properties of a q-analogue of Bessel functions, under preparation.
19. M.E.H. Ismail and M. Rahman, "The associated Askey-Wilson polynomials," Trans. Amer. Math. Soc. 328 (1991), 201-237.
20. M.E.H. Ismail, M. Rahman, and D. Stanton, "Quadratic q-exponentials and connection coefficient problems," Proc. Amer. Math. Soc. 127(10) (1999), 2931-2941.
21. M.E.H. Ismail, M. Rahman, and S.K. Suslov, "Some summation theorems and transformations for q-series," Can. J. Math. 49 (1997), 543-567.
22. M.E.H. Ismail, M. Rahman, and R. Zhang, "Diagonalization of certain integral operators II," J. Comp. Appl. Math. 68 (1996), 163-196.
23. M.E.H. Ismail and D.W. Stanton, "Addition theorems for the q-exponential functions," in q-Series from a Contemporary Perspective, Vol. 254: Contemporary Mathematics (M.E.H. Ismail and D.R. Stanton, eds.). American Mathematical Society, 2000, pp. 235-245.
24. 4φ3-polynomials," J. Approx. Theory 36 (1982), 43-54.
25. M.E.H. Ismail and R. Zhang, "Diagonalization of certain integral operators." Advances in Math. 108 (1994), 1-33.
26. R. Koekoek and R.F. Swarttouw, "The Askey scheme of hypergeometric orthogonal polynomials and its q-analogues," Report 94-05, Delft University of Technology, 1994.
27. 1 (Ithaca, 1993), J. Symbolic Comput. 20(5-6) (1995), 737-744.
28. B. Ya. Levin, "Distribution of Zeros of Entire Functions," Translations of Mathematical Monographs, Vol. 5, Amer. Math. Soc., Providence, Rhode Island, 1980.
29. A.F. Nikiforov, S.K. Suslov, and V.B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable, Nauka, Moscow, 1985 [in Russian]: English translation, Springer-Verlag, Berlin, 1991.
30. M. Rahman, "q-Wilson functions of the second kind," SIAM J. Math. Anal. 17 (1986), 1280-1286.
31. 2(x; β | q)," J. Math. Anal. Appl. 164 (1992), 263-284.
32. M. Rahman, "A q-extension of a product formula of Watson." Quaestiones Mathematicae 22 (1999), 27-42.
33. M. Rahman and S.K. Suslov, "The Pearson equation and beta integrals," SIAM J. Math. Anal. 25 (1994). 646-693.
34. M. Rahman and S.K. Suslov, "Barnes and Ramanujan-type integrals on the q-linear lattice," SIAM J. Math. Anal. 25 (1994), 1002-1022.
35. S.K. Suslov, "The theory of difference analogues of special functions of hypergeometric type," Russian Math. Surveys 44 (1989), 227-278.
36. S.K. Suslov, "Addition theorems for some q-exponential and q-trigonometric functions," Methods and Applications of Analysis 4 (1997), 11-32.
37. 8φ7-functions," J. Phys. A: Math. Gen. 30 (1997), 5877-5885.
38. S.K. Suslov, "Some expansions in basic Fourier series and related topics," Journal of Approximation Theory, to appear.
39. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd edn., Cambridge University Press, Cambridge, 1944.