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)
Some bounding inequalities for the Jacobi and related functions. (English) Zbl 1131.26005
The paper describes establishment of bounding inequalities for the Jacobi function as a consequence of reasonably sharp inequalities for the classical Laguerre functions, given in Section 2 of the paper in the form of four lemmas. By virtue of hypergeometric representations of the classical Jacobi function P υ (α,β) (z) (υC) of the first kind and the classical Laguerre function L υ (μ) (z) (υC) in terms of 1 F 1 (·), the Eulerian integral is written and then appealing to the corresponding version of Love’s inequality, the first bounding inequality is obtained. Further, the lemmas those given in Section 2 are employed to obtain remaining two bounding inequalities.
MSC:
26A33Fractional derivatives and integrals (real functions)
33C45Orthogonal polynomials and functions of hypergeometric type
26D15Inequalities for sums, series and integrals of real functions
33C15Confluent hypergeometric functions, Whittaker functions, 1 F 1