zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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 expansion of a multiple integral. (English) Zbl 0636.41024

Die Verff. betrachten die asymptotische Entwicklung des Integrals

J(s)= 0 1 0 1 g(x a y b /s)x α y β f(x,y)dxdy

für s+0. Mittels Mellin Transformation wird J(s) durch das Integral J(s)=(1/2πi) c-i c+i s -z F(z)M[g,-z]dz dargestellt. Danach gibt die Verschiebung des Weges nach links die gesuchte Entwicklung. Die Hauptaufgabe ist die Eigenschaften des Integrals F(z)= 0 1 0 1 x α+az y β+bz f(x,y)dxdy in der Z-Ebene zu untersuchen. Es wird gezeigt, daß F(z) eine meromorphe Funktion ist, und die Residuen werden berechnet.

Reviewer: E.Riekstinš
MSC:
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
44A15Special transforms (Legendre, Hilbert, etc.)