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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Recurrence relations for hypergeometric functions of unit argument


Author: Stanisław Lewanowicz
Journal: Math. Comp. 45 (1985), 521-535
MSC: Primary 33A35; Secondary 65Q05
Corrigendum: Math. Comp. 48 (1987), 853.
Corrigendum: Math. Comp. 48 (1987), 853-854.
MathSciNet review: 804941
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the generalized hypergeometric function

$\displaystyle {P_n}:{ = _{p + 3}}{F_{p + 2}}\left( {\left. {\begin{array}{*{20}... ...} \\ {{b_{p + 2}}} \\ \end{array} } \right\vert 1} \right)\quad (n \geqslant 0)$

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

$\displaystyle {U_n}: = \frac{{{{({c_{q + 1}})}_n}}}{{{{({d_q})}_n}{{(n + \lambd... ...,2n + \lambda + 1} \\ \end{array} } \right\vert 1} \right)\quad (n \geqslant 0)$

a homogeneous recurrence relation of order $ q + 1$ is given.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1985-0804941-2
PII: S 0025-5718(1985)0804941-2
Article copyright: © Copyright 1985 American Mathematical Society