zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Asymptotic formulas for the zeros of the Meixner polynomials. (English) Zbl 0931.33006
In the paper under review interesting asymptotic results are given for the zeros of the Meixner polynomials. Large zeros and small zeros are discussed separately, and it is shown by numeric examples that the given estimates are quite accurate in some situations.

33C45Orthogonal polynomials and functions of hypergeometric type
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
Full Text: DOI
[1] Abramowitz, M.; Stegun, I.: Handbook of mathematical functions. Appl. math. Ser. 55 (1964) · Zbl 0171.38503
[2] Bo, R.; Wong, R.: Asymptotic behavior of the pollaczek polynomials and their zeros. Stud. appl. Math. 96, 307-338 (1996) · Zbl 0859.41025
[3] Chen, Y.; Ismail, M. E. H.: Asymptotics of extreme zeros of the meixner--pollaczek polynomials. J. comput. Appl. math. 82, 59-78 (1997) · Zbl 0902.33004
[4] Hethcote, H. W.: Error bounds for asymptotic approximations of zeros of transcendental functions. SIAM J. Math. anal. 1, 147-152 (1970) · Zbl 0199.49902
[5] Ismail, M. E. H.: Asymptotics of pollaczek polynomials and their zeros. SIAM J. Math. anal. 25, 462-473 (1994) · Zbl 0805.33005
[6] M. E. H. Ismail, On the largest zeros of Meixner polynomials, 1996
[7] Ismail, M. E. H.; Li, Xin: Bound on the extreme zeros of orthogonal polynomials. Proc. amer. Math. soc. 115, 131-140 (1992) · Zbl 0744.33005
[8] Jin, X. -S.; Wong, R.: Uniform asymptotic expansions for meixner polynomials. Constr. approx. 14, 113-150 (1998) · Zbl 0906.41020
[9] Novikoff, A.: On a special system of polynomials. (1954)
[10] Olver, F. W. J.: Uniform asymptotic expansions for Weber parabolic cylinder functions of large order. J. res. Nat. bur. Standards sect. B 63, 131-169 (1959) · Zbl 0090.04602
[11] Olver, F. W. J.: Asymptotics and special functions. (1974) · Zbl 0303.41035
[12] Szegö, G.: Orthogonal polynomials. Colloq. publ. 23 (1975) · Zbl 0305.42011