# 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)
Uniform asymptotic smoothing of Stokes’ discontinuities. (English) Zbl 0683.33004
Stokes’ discontinuities occur in the asymptotic approximation of functions defined by integrals or differential equations and dependent on a large complex parameter $\lambda$. Usually several asymptotic estimates are available in different sectors of the complex $\lambda$-plane. At the border lines of the sectors, usually called Stokes lines, the change in the approximations is not always smooth; the jumps may be exponentially large. If the expansion is truncated near its least term, the change may be smooth, and can be described in terms of an error function. This new interpretation introduces an interesting development in the theory of asymptotic expansions. The author uses the formalism of Dingle to describe the phenomenon, and he gives numerical illustrations for Dawson’s integral and Airy functions.
Reviewer: N.M.Temme

##### MSC:
 33B20 Incomplete beta and gamma functions 30E15 Asymptotic representations in the complex domain 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
##### Keywords:
Stokes’ phenomenon; error function