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)
Gamma function asymptotics by an extension of the method of steepest descents. (English) Zbl 0829.33001
The paper deals with the usual asymptotic expansion of the $\Gamma$- function, $$\Gamma(z)= \sqrt {2\pi} \exp \bigl\{ (z- {\textstyle {1\over 2}}) \log z-z \bigr\} \Biggl\{ \sum_{k=0}^{n-1} {\textstyle {a_k \over z^k}}+ R_N (z) \Biggr\} \qquad \text{as }z\to \infty \quad \text{in } |\arg (z)|<\pi.$$ Based on the recent work of {\it M. V. Berry} and {\it C. J. Howls} [Proc. R. Soc., Lond., Ser. A 434, No. 1892, 657-675 (1991; Zbl 0764.30031)] the author derives integral formulas for the coefficients $a_k$ and the remainder term $R_N (z)$. As a result he obtains explicit and good bounds for the remainder terms of the Stokes line $\text{Re} (z)= {\pi\over 2}$, the transition formula connecting the different asymptotic relations and the asymptotic behaviour of the coefficients $a_k$ as $k\to \infty$.

33B15Gamma, beta and polygamma functions
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
Full Text: DOI