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)
Error analysis in a uniform asymptotic expansion for the generalised exponential integral. (English) Zbl 0870.33002
Summary: Uniform asymptotic expansions are derived for the generalised exponential integral E p (z), where both p and z are complex. These are derived by examining the differential equation satisfied by E p (z), an equation which possesses a double turning point at z/p=-1. The expansions, which involve the complementary error function, together approximate E p (z) as |p|, uniformly for all non-zero complex z satisfying 0arg(z/p)2π. The error terms associated with the truncated expansions are shown to be solutions of inhomogeneous differential equations, and from these explicit and realistic bounds are derived. By employing the maximum-modulus theorem the bounds are then simplified to make them more conductive to numerical evaluation.
33B20Incomplete beta and gamma functions
34E20Asymptotic singular perturbations, turning point theory, WKB methods (ODE)
34E05Asymptotic expansions (ODE)
30E10Approximation in the complex domain
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)