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Zbl 0583.33005
Lewanowicz, Stanisław
Recurrence relations for hypergeometric functions of unit argument. (English)
[J] Math. Comput. 45, 521-535 (1985). ISSN 0025-5718; ISSN 1088-6842/e

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.
[S.L.Kalla]

MSC 2000:: *33C05 Classical hypergeometric functions
65D20 Computation of special functions
65Q05 Numerical methods for functional equations

Keywords: recurrence relation

Citations: Zbl 0186.104; Zbl 0304.33003; Zbl 0193.017

Cited in: Zbl 0612.33003

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