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)
Coefficient functions for an inhomogeneous turning-point problem. (English) Zbl 0754.34059
The author considers the differential equation (1) d 2 W/dζ 2 -{u 2 ζ+ψ(ζ)}W=ω ¯(ζ), where ψ(ζ) and ω ¯(ζ) are holomorphic in a simple connected domain Δ which includes the turning-point ζ=0, and u is a large positive parameter. This is a slightly less general equation than that considered by Clark and by Oliver. The author uses Boyd’s approach to calculate bounds for the error term ε 2n+1 (u,ζ) and proves that a necessary and sufficient condition for W(u,ζ) to be a solution of (1) is that W(u,ζ)=u -4/3 𝒜(u,ζ)S(u 2/3 ζ)+u -8/3 (u,ζ)S ' (u 2/3 ζ)+u -2 𝒞(u,ζ), for some solution S(z) of the differential equation d 2 S/dz 2 -zS=1.
Reviewer: H.S.Nur (Fresno)
34E20Asymptotic singular perturbations, turning point theory, WKB methods (ODE)
34E05Asymptotic expansions (ODE)
34K25Asymptotic theory of functional-differential equations
34M99Differential equations in the complex domain