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

 

An analytic method for convergence acceleration of certain hypergeometric series


Authors: Stanisław Lewanowicz and Stefan Paszkowski
Journal: Math. Comp. 64 (1995), 691-713
MSC: Primary 33C45; Secondary 65B10, 65D20
MathSciNet review: 1277769
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Abstract: A method is presented for convergence acceleration of the generalized hypergeometric series $ _3{F_2}$ with the argument $ \pm 1$, using analytic properties of their terms. Iterated transformation of the series is performed analytically, which results in obtaining new fast converging expansions for some special functions and mathematical constants.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1995-1277769-6
PII: S 0025-5718(1995)1277769-6
Keywords: Analytic convergence acceleration, generalized hypergeometric series, polygamma functions, Beta function
Article copyright: © Copyright 1995 American Mathematical Society