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)
Uniform asymptotic expansions for associated Legendre functions of large order. (English) Zbl 1055.33008
There is an extensive literature on the asymptotic behavior of the associated Legendre functions. This paper fills the gap by treating uniform expansions for large order and small to large degree, both real. The following cases are covered: 1. Fixed $\nu$, complex argument Method: as in [{\it F. W. J. Olver}, Introduction to asymptotics and special functions (1974; Zbl 0308.41023), chapter 12]. 2. Small to large $\nu$, complex argument Method: the Liouville transform from {\it W. G. C. Boyd} and {\it T. M. Dunster} [SIAM J. Math. Anal. 17, 422--450 (1986; Zbl 0591.34048)]. 3. Small to large $\nu$, real argument in $(-1,1)$ for Ferrer’s function Method: Liouville transform and results from Olver [loc. cit.]. A well written paper.
33C45Orthogonal polynomials and functions of hypergeometric type
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
Full Text: DOI