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 language | English |
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Pages (from-to) | 1443–1457 |
Number of pages | 15 |
Journal | Results in Mathematics |
Volume | 71 |
Issue number | 3-4 |
Early online date | 12 Oct 2016 |
DOIs | |
Publication status | Published - Jun 2017 |
Keywords
- Completely monotonic functions
- Bernoulli polynomials and numbers
- Euler polynomials and numbers