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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Series Representation
Remainder
Completely Monotonic Function
Bernoulli numbers
Gamma function
Recurrence relation
Deduce

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Chen, Chao-Ping ; Paris, Richard B. / Series representations of the remainders in the expansions for certain functions with applications. In: Results in Mathematics. 2017 ; Vol. 71, No. 3-4. pp. 1443–1457.
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Series representations of the remainders in the expansions for certain functions with applications. / Chen, Chao-Ping; Paris, Richard B.

In: Results in Mathematics, Vol. 71, No. 3-4, 06.2017, p. 1443–1457.

Research output: Contribution to journalArticle

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