Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On a sequence transformation with integral coefficients for Euler’s constant
HTML articles powered by AMS MathViewer

by C. Elsner PDF
Proc. Amer. Math. Soc. 123 (1995), 1537-1541 Request permission

Abstract:

Let $\gamma$ denote Euler’s constant, and let \[ {s_n} = \left ( {1 + \frac {1}{2} + \cdots + \frac {1}{{n - 1}}} \right ) - \log n\quad (n \geq 2).\] We prove by Ser’s formula for the remainder $\gamma - {s_n}$ that for all integers $n \geq 1$ and $\tau \geq 2$ there are integers ${\mu _{n,0,}}{\mu _{n,1}}, \ldots ,{\mu _{n,n}}$ such that \[ {\mu _{n,0}}{s_\tau } + {\mu _{n,1}}{s_{\tau + 1}} + \cdots + {\mu _{n,n}}{s_{\tau + n}} = \gamma + {O_\tau }({(n(n + 1)(n + 2) \bullet \cdots \bullet (n + \tau ))^{ - 1}}),\] where the constant in ${O_\tau }$ depends only on $\tau$. The coefficients ${\mu _{n,k}}$ are explicitly given and are bounded by ${2^{3n + \tau - 1}}$.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11Y60, 40A05, 65B05
  • Retrieve articles in all journals with MSC: 11Y60, 40A05, 65B05
Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1537-1541
  • MSC: Primary 11Y60; Secondary 40A05, 65B05
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1233969-4
  • MathSciNet review: 1233969