Series representations of the remainders in the expansions for certain functions with applications

Chao-Ping Chen, Richard B. Paris

    Research output: Contribution to journalArticle

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    Abstract

    We present a summary of the series representations of the remainders in the expansions in ascending powers of t of 2/(et+1), sech t and coth t and establish simple bounds for these remainders when t>0. Several applications of these expansions are given which enable us to deduce some inequalities and completely monotonic functions associated with the ratio of two gamma functions. In addition, we derive a (presumably new) quadratic recurrence relation for the Bernoulli numbers Bn.
    Original languageEnglish
    Pages (from-to)1443–1457
    Number of pages15
    JournalResults in Mathematics
    Volume71
    Issue number3-4
    Early online date12 Oct 2016
    DOIs
    Publication statusPublished - Jun 2017

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