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)
Recurrence relations for hypergeometric functions of unit argument. (English) Zbl 0583.33005
The author shows that the generalized hypergeometric function $$ P\sb n := {}\sb{p+3}F\sb{p+2} \pmatrix -n,n+\lambda,a\sb p,1\\ &;1 \\ b\sb{p+2} \endpmatrix, \quad n\ge 0 $$ satisfies a nonhomogeneous recurrence relation of order p, when $\sb{p+3}F\sb{p+2}(1)$ is balanced, and of order $p+1$ otherwise. For $$ U\sb n := ((c\sb{q+1})\sb n/(d\sb q)\sb n(n+\lambda)\sb n)\sb{q+2} F\sb{q+1} \pmatrix n+c\sb{q+2} \\ &;1 \\ n+d\sb q,2n+\lambda +1 \endpmatrix, \quad n\ge 0 $$ a homogeneous recurrence relation of order $q+1$ is given. The results are proved by using some general theorems due to {\it J. Wimp} [Math. Comput. 22, 363-373 (1968; Zbl 0186.104); ibid. 29, 577-581 (1975; Zbl 0304.33003)] and {\it Y. Luke} [The special functions and their approximations (1969; Zbl 0193.017)]. Some examples are given.
Reviewer: S.L.Kalla

33C05Classical hypergeometric functions, ${}_2F_1$
65D20Computation of special functions, construction of tables
65Q05Numerical methods for functional equations (MSC2000)
Full Text: DOI