Abstract
| Original language | English |
|---|---|
| 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 |
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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 journal › Article
TY - JOUR
T1 - Series representations of the remainders in the expansions for certain functions with applications
AU - Chen, Chao-Ping
AU - Paris, Richard B.
PY - 2017/6
Y1 - 2017/6
N2 - 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.
AB - 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.
U2 - 10.1007/s00025-016-0612-1
DO - 10.1007/s00025-016-0612-1
M3 - Article
VL - 71
SP - 1443
EP - 1457
JO - Results in Mathematics
JF - Results in Mathematics
SN - 1422-6383
IS - 3-4
ER -