Vol. 14, No. 5, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16, 1 issue

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
 
Other MSP Journals
On the coefficients in an asymptotic expansion of $(1+1/x)^x$

T. M. Dunster and Jessica M. Perez

Vol. 14 (2021), No. 5, 775–781
Abstract

The function g(x) = (1 + 1x)x has the well-known limit e as x . The coefficients cj in an asymptotic expansion for g(x) are considered. A simple recursion formula is derived, and then using Cauchy’s integral formula the coefficients are approximated for large j. From this it is shown that |cj| 1 as j .

Keywords
series expansions, asymptotic representations in the complex plane, integrals of Cauchy type
Mathematical Subject Classification
Primary: 41A58, 30E15, 30E20
Milestones
Received: 12 May 2020
Accepted: 8 May 2021
Published: 9 February 2022

Communicated by Kenneth S. Berenhaut
Authors
T. M. Dunster
Department of Mathematics and Statistics
San Diego State University
San Diego, CA
United States
Jessica M. Perez
Department of Mathematics and Statistics
San Diego State University
San Diego, CA
United States