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# Recurrence Relations for Hypergeometric Functions of Unit Argument

Stanisław Lewanowicz
Mathematics of Computation
Vol. 45, No. 172 (Oct., 1985), pp. 521-535
DOI: 10.2307/2008142
Stable URL: http://www.jstor.org/stable/2008142
Page Count: 15
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## Abstract

We show that the generalized hypergeometric function \begin{equation*}P_n:=_{p + 3}F_{p + 2}\Bigg(\overset{-n, n + \lambda, a_p, 1}{b_{p + 2}} \Bigg| 1\Bigg)\quad (n \geq 0)\end{equation*} satisfies a nonhomogeneous recurrence relation of order $p + \sigma$, where $\sigma = 0$ when $_{p + 3}F_{p + 2}(1)$ is balanced, and $\sigma = 1$ otherwise. Also, for \begin{equation*}U_n:= \frac{(c_{q + 1})_n}{(d_q)_n(n + \lambda)_n}_{q + 2}F_{q + 1}\Bigg(\overset{n + c_{q + 2}}{n + d_q, 2n + \lambda + 1}\Bigg| 1\Bigg)\quad (n \geq 0)\end{equation*} a homogeneous recurrence relation of order $q + 1$ is given.

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