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)
Computing toroidal functions for wide ranges of the parameters. (English) Zbl 0994.65018
Summary: Associated Legendre functions of half-odd degree and arguments larger than one, also known as toroidal harmonics, appear in the solution of Dirichlet problems with toroidal symmetry. It is shown how the use of series expansions, continued fractions, and uniform asymptotic expansions, together with the application of recurrence relations over degrees and orders, permits the evaluation of the whole set of toroidal functions for a wide range of arguments, orders, and degrees. In particular, we provide a suitable uniform asymptotic expansion for P m (x) (for large m), which fills the gap left by previous methods.
MSC:
65D20Computation of special functions, construction of tables
33C47Other special orthogonal polynomials and functions