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A new fast asymptotic series for the gamma function

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Abstract

It is the scope of this paper to present a new formula for approximating the gamma function. The importance of this new formula consists in the fact that the convergence of the corresponding asymptotic series is very fast in comparison with other classical or recently discovered asymptotic series. Inequalities related to this new formula and asymptotic series are established. Some conjectures are proposed.

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Acknowledgments

Part of this work was completed during the author’s visit at Moldova State University in Chişin\(\breve{\mathrm{a}}\)u, Republic of Moldova. Some computations made in this paper were performed using Maple software. The author thanks the anonymous referee for valuable comments and corrections which improved much the first form of this paper.

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Authors and Affiliations

  1. Valahia University of Târgovişte, Bd. Unirii 18, 130082 , Târgovişte, Romania

    Cristinel Mortici

  2. Academy of Romanian Scientists, Splaiul Independenţei 54, 050094 , Bucharest, Romania

    Cristinel Mortici

Authors
  1. Cristinel Mortici
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Correspondence to Cristinel Mortici.

Additional information

This work was supported by a Grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, Project Number PN-II-ID-PCE-2011-3-0087.

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Mortici, C. A new fast asymptotic series for the gamma function. Ramanujan J 38, 549–559 (2015). https://doi.org/10.1007/s11139-014-9589-0

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  • DOI: https://doi.org/10.1007/s11139-014-9589-0

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