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 the representation of Meijer’s G-function in the vicinity of singular unity. (English) Zbl 0581.33006
Complex analysis and applications, Proc. Int. Conf., Varna/Bulg. 1981, 383-398 (1984).
[For the entire collection see Zbl 0573.00007.] Although the behaviors of Meijer’s G-function at the singular points 0 and $\infty$ have been explored in the case $p=q$, little information in regard to the behavior at the singular point $z=(-1)\sp{m+n-p}$ has been available. This function is one solution of a certain p-th order linear differential equation. In the present paper a fundamental system of solutions in the neighbourhood of this critical point is found. The explicit, but very complicated, representations are obtained and the recurrences for the coefficients are included. The complicated situation in regard to this G-function in a neighborhood of $z=(-1)\sp{m+n-p}$ can now be better understood. The asymptotic behavior as $z\to 1$ is determined and a set of simple, explicit special cases is appended in order to display all of the various behaviors. Further, some new relations are included which connect G-functions with different parameters.
Reviewer: R.G.Buschman
33C60Hypergeometric integrals and functions defined by them
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)