Accelerating Dougall’s $_5F_4$-sum and infinite series involving $\pi $
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Publication:2862541
DOI10.1090/S0025-5718-2013-02701-9zbMath1282.33024OpenAlexW1540386574MaRDI QIDQ2862541
Publication date: 15 November 2013
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0025-5718-2013-02701-9
hypergeometric seriespartial sumssummation by partsAbel's lemmaacceleration of convergent seriesDougall's \({}_5H_5\)-series
Exact enumeration problems, generating functions (05A15) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)
Related Items (22)
Infinite series identities derived from the very well-poised \(\Omega\)-sum ⋮ Hidden \(q\)-analogues of Ramanujan-like \(\pi\)-series ⋮ Formulas for generalized two-qubit separability probabilities ⋮ Multiple-correction and continued fraction approximation. II ⋮ Infinite series formulae related to Gauss and Bailey \(_2F_1(\frac{1}{2})\)-sums ⋮ Dougall's \(_5F_4\) sum and the WZ algorithm ⋮ \(q\)-difference equations for Askey-Wilson type integrals via \(q\)-polynomials ⋮ Series acceleration formulas obtained from experimentally discovered hypergeometric recursions ⋮ A series evaluation technique based on a modified Abel lemma ⋮ ON GUILLERA’S -SERIES FOR ⋮ INFINITE SERIES CONCERNING HARMONIC NUMBERS AND QUINTIC CENTRAL BINOMIAL COEFFICIENTS ⋮ Infinite series about harmonic numbers inspired by Ramanujan-like formulae ⋮ \( \pi \)-formulas from dual series of the Dougall theorem ⋮ Summation formulas on harmonic numbers and five central binomial coefficients ⋮ Infinite series of convergence rate $-1/8$ suggested by two formulae of Guillera ⋮ Unnamed Item ⋮ Further Apéry-like series for Riemann zeta function ⋮ $q$-analogues of several $\pi $-formulas ⋮ Alternating series of Apéry-type for the Riemann zeta function. ⋮ Ramanujan-like formulae for \(\pi\) and \(1/\pi\) via Gould-Hsu inverse series relations ⋮ q-Analogues of Guillera’s two series for π±2 with convergence rate 27 64 ⋮ Common extension of the Watson and Whipple sums and Ramanujan-likeπ-formulae
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