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

Chao-Ping Chen; Richard B. Paris

doi:10.1007/s00025-016-0612-1

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

Chao-Ping Chen, Richard B. Paris

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

112 Downloads (Pure)

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 B_n.

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	https://doi.org/10.1007/s00025-016-0612-1
Publication status	Published - Jun 2017

Access to Document

10.1007/s00025-016-0612-1

Paris_SeriesRepresentations_Accepted_2016Accepted author manuscript, 315 KB

Fingerprint Dive into the research topics of 'Series representations of the remainders in the expansions for certain functions with applications'. Together they form a unique fingerprint.

Cite this

@article{1f0a8fc20b984fe7bdb4b2b39eeacb8a,

title = "Series representations of the remainders in the expansions for certain functions with applications",

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.",

author = "Chao-Ping Chen and Paris, {Richard B.}",

year = "2017",

month = jun,

doi = "10.1007/s00025-016-0612-1",

language = "English",

volume = "71",

pages = "1443–1457",

journal = "Results in Mathematics",

issn = "1422-6383",

publisher = "Birkhauser Verlag Basel",

number = "3-4",

}

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 -