Asymptotic Formulas for the Zeros of the Meixner Polynomials

Journal of Approximation Theory

Volumn 96, Issue 2, 1999, Pages 281-300

  Jin, X S ^a   Wong, R ^b  

^a UNIVERSITY OF MANITOBA   (Canada)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000049933     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1998.3235     Document Type: Article

References (12)

1. M. Abramowitz and I. Stegun (Eds.), "Handbook of Mathematical Functions", Appl. Math. Ser., Vol. 55, National Bureau of Standards, Washington, DC, 1964.
2. R. Bo and R. Wong, Asymptotic behavior of the Pollaczek polynomials and their zeros, Stud. Appl. Math. 96 (1996), 307-338.
3. Y. Chen and M. E. H. Ismail, Asymptotics of extreme zeros of the Meixner-Pollaczek polynomials, J. Comput. Appl. Math. 82 (1997), 59-78.
4. H. W. Hethcote, Error bounds for asymptotic approximations of zeros of transcendental functions, SIAM J. Math. Anal. 1 (1970), 147-152.
5. M. E. H. Ismail, Asymptotics of Pollaczek polynomials and their zeros, SIAM J. Math. Anal. 25 (1994), 462-473.
6. M. E. H. Ismail, On the largest zeros of Meixner polynomials, manuscript, 1996.
7. M. E. H. Ismail and Xin Li, Bound on the extreme zeros of orthogonal polynomials, Proc. Amer. Math. Soc. 115 (1992), 131-140.
8. X.-S. Jin and R. Wong, Uniform asymptotic expansions for Meixner polynomials, Constr. Approx. 14 (1998), 113-150.
9. A. Novikoff, "On a Special System of Polynomials", Ph.D. dissertation, Stanford University, Stanford, CA, 1954.
10. F. W. J. Olver, Uniform asymptotic expansions for Weber parabolic cylinder functions of large order, J. Res. Nat. Bur. Standards Sect. B 63 (1959), 131-169.
11. F. W. J. Olver, "Asymptotics and Special Functions", Academic Press, New York, 1974.
12. G. Szegö, "Orthogonal Polynomials", 4th ed., Colloq. Publ., Vol. 23, Amer. Math. Soc., Providence, RI, 1975.