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)
On an integral transform involving a class of Mathieu functions. (English) Zbl 0685.44003
The author develops an inversion formula associated with the integral transform F(u) defined by the equation F(u)= a f(x)ψ(x,u)dx, where ψ (x,u) denotes the Mathieu function of the third kind M r (3) (x+iπ) which satisfies the modified form of Mathieu’s equation ψ xx =(u 2 +2h 2 cosh2x)ψ, h being a positive constant. The basic inversion formula is expressed as an integral in the complex u-plane and applies for functions f(x) such that e -λx f(x)L 2 (a,) where λ0. An explicit eigenfunction expansion is obtainable for the case λ=0.
Reviewer: D.Naylor
44A15Special transforms (Legendre, Hilbert, etc.)
34L99Ordinary differential operators
33E10Lamé, Mathieu, and spheroidal wave functions