On the asymptotics of the Meixner-Pollaczek polynomials and their zeros

Constructive Approximation

Volumn 17, Issue 1, 2001, Pages 59-90

  Li, X ^a   Wong, R ^b  

^a Beijing Institute of Printing   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Meixner Pollaczek polynomials; Parabolic cylinder functions; Uniform asymptotic expansions; Zeros

Indexed keywords

EID: 0035529227     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003650010009     Document Type: Article

References (21)

1. M. ABRAMOWITZ, I. STEGUN (eds.) (1964): Handbook of Mathematical Functions. Applied Mathematics Series, Vol. 55. Washington, DC: National Bureau of Standards. (Paperback edition published by Dover, New York.)
2. C. M. BENDER, L. R. MEAD, S. S. PINSKY (1987): Continuous Hahn polynomials and the Heisenberg algebra. J. Math. Phys., 28:509-513.
3. BO RUI, R. WONG (1994): Uniform asymptotic expansion of Charlier polynomials. Methods Appl. Anal., 1:294-313.
4. BO RUI, R. WONG (1996): Asymptotic behavior of the Pollaczek polynomials and their zeros. Stud. Appl. Math., 96:307-338.
5. Y. CHEN, M. E. H. ISMAIL (1997):Asymptotics of extreme zeros of the Meixner-Pollaczek polynomials. J. Comput. Appl. Math., 82:59-78.
6. T. S. CHIHARA (1978): An Introduction to Orthogonal Polynomials. New York: Gordon and Breach.
7. A. ERDÉLYI (1960): Asymptotic forms for Laguerre polynomials. J. Indian Math. Soc. (Golden Jubilee Commemorative Volume), 24:235-250.
8. V. FREILIKHER, E. KANZIEPER, I. YURKEVICH (1996): Unitary random-matrix ensemble with governable level confinement. Phys. Rev. E, 53:2200-2209.
9. C. L. FRENZEN, R. WONG (1988): Uniform asymptotic expansions of Laguerre polynomials. SIAM J. Math. Anal., 19:1232-1248.
10. H. W. HETHCOTE (1970): Error bounds for asymptotic approximations of zeros of transcendental functions. SIAM J. Math. Anal., 1:147-152.
11. M. E. H. ISMAIL, X. LI (1992): Bound on the extreme zeros of orthogonal polynomials. Proc. Amer. Math. Soc., 115:131-140.
12. X.-S. JIN, R. WONG (1998): Uniform asymptotic expansions for Meixner polynomials. Constr. Approx., 14:113-150.
13. X.-S. JIN, R. WONG (1999): Asymptotic formulas for the zeros of the Meixner polynomials. J. Approx. Theory, 96:281-300.
14. T. H. KOORWINDER (1989): Meixner-Pollaczek polynomials and the Heisenberg algebra. J. Math. Phys., 30:767-769.
15. A. I. MARKUSHEVICH (1977): Theory of Functions of a Complex Variable. 2nd ed. New York: Chelsea.
16. D. R. MASSON (1989): Some continuous fractions of Ramanujan and Meixner-Pollaczek polynomials. Canad. Math. Bull., 32:177-181.
17. F. W. J. OLVER (1959): Uniform asymptotic expansions for Weber parabolic cylinder functions of large order. J. Res. Nat. Bur. Standards, Sect. B, 63:131-169.
18. F. W. J. OLVER (1974): Asymptotics and Special Functions. New York: Academic Press.
19. G. SZEGÖ (1975): Orthogonal Polynomials. 4th ed. Colloquium Publications, Vol. 23. Providence, RI: American Mathematical Society.
20. R. WONG (1989): Asymptotic Approximations of Integrals. Boston: Academic Press.
21. J. ZENG (1992): Weighted derangements and the linearization coefficients of orthogonal Sheffer polynomials. Proc. London Math. Soc., 65:1-22.