Analytical and asymptotic representations for two sequence related to Gauss’ lemniscate functions-Reference-Cited by-同舟云学术

Analytical and asymptotic representations for two sequence related to Gauss’ lemniscate functions

Published:2023 Issue:2 Volume:17 Page:525-537
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, 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

Let the sequences Gn and gn be defined by Gn := ?10 dt/(1?t2n)1/n (n ? 2) and gn := ??0 dt/(1 + t2n)1/n (n ? 1). In this paper, we first derive analytical representations for these two sequences Gn and gn in terms of the gamma function. By using the obtained analytical representations, we then deduce asymptotic expansions for Gn and gn.

Publisher

National Library of Serbia

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

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