On Some Series Dependent on a Parameter Which Generalize Euler’s Constant

Authors

  • Paul Bracken University of Texas

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i1.3346

Keywords:

Euler’s constant, sequence, series, convergence, asymptotic

Abstract

Series which depend on a parameter and generalize the constant discovered by Euler are introduced and studied. Convergence results are established. An infinite series expansion is obtained from these generalized formulas which can be used to evaluate the generalized constant. Euler’s constant can be obtained as a special case. Some asymptotic results are formulated and limits of some closely related sequences are given at the end.

Author Biography

  • Paul Bracken, University of Texas
    Mathematics/Physics

Downloads

Published

2019-01-31

Issue

Vol. 12 No. 1: (January 2019)

Section

Discrete Mathematics

License

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

On Some Series Dependent on a Parameter Which Generalize Euler’s Constant. (2019). European Journal of Pure and Applied Mathematics, 12(1), 1-13. https://doi.org/10.29020/nybg.ejpam.v12i1.3346