Asymptotic expansions for the Wallis sequence and some new mathematical constants associated with the Glaisher-Kinkelin and Choi-Srivastava constants-Reference-Cited by-同舟云学术

Asymptotic expansions for the Wallis sequence and some new mathematical constants associated with the Glaisher-Kinkelin and Choi-Srivastava constants

Published:2022 Issue:00 Volume: Page:24-24
ISSN:1452-8630
Container-title:Applicable Analysis and Discrete Mathematics
language:en
Short-container-title:APPL ANAL DISCRETE M

Author:

Han Xue-Feng¹,Chen Chao-Ping²,Srivastava H.M.³

Affiliation:

1. School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, People’s Republic of China

2. School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City , Henan Province, People’s Republic of China

3. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia VW R, Canada + Department of Medical Research, China Medical University Hospital, China + Medical University, Taichung, Taiwan, Republic of China + Department of Mathematics and Informatics, Azerbaijan University, Baku, Azerbaijan + Section of Mathematics, International Telematic University Uninettuno, Rome, Italy

Abstract

The celebrated Wallis sequence Wn, which is defined by Wn := ?nk=1 4k2/4k2?1, is known to have the limit ? 2 as n ? ?. Without using the Bernoulli numbers Bn, the authors present several asymptotic expansions and a recurrence relation for determining the coefficients of each asymptotic expansion related to the Wallis sequence Wn and the newly-introduced constants D and E, which are analogous to the Glaisher-Kinkelin constant A and the Choi-Srivastava constants B and C.

Publisher

National Library of Serbia

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis