Ramanujan Summation for Powers of Triangular and Pronic Numbers-Reference-Cited by-同舟云学术

Ramanujan Summation for Powers of Triangular and Pronic Numbers

Published:2020-12-30 Issue:1-2 Volume:5 Page:05-08
ISSN:2456-799X
Container-title:Oriental Journal of Physical Sciences
language:
Short-container-title:Orient J Phys Sciences

Author:

Sivaraman Dr. R.¹^ORCID

Affiliation:

1. 1Independent Research Scholar, African Moon University, South West Africa and USA .

Abstract

The numbers which are sum of first n natural numbers are called Triangular numbers and numbers which are product of two consecutive positive integers are called Pronic numbers. The concept of Ramanujan summation has been dealt by Srinivasa Ramanujan for divergent series of real numbers. In this paper, I will determine the Ramanujan summation for positive integral powers of triangular and Pronic numbers and derive a new compact formula for general case.

Publisher

Oriental Scientific Publishing Company

Subject

Management Science and Operations Research,Mechanical Engineering,Energy Engineering and Power Technology

Reference8 articles.

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2. R. Sivaraman, Remembering Ramanujan, Advances in Mathematics: Scientific Journal, Volume 9 (2020), no.1, 489–506.

3. S. Ramanujan, Manuscript Book 1 of Srinvasa Ramanujan, First Notebook, Chapter VIII, 66–68.

4. Bruce C. Berndt, Ramanujan’s Notebooks Part II, Springer, Corrected Second Edition, 1999.

5. G.H. Hardy, J.E. Littlewood, Contributions to the theory of Riemann zeta-function and the theory of distribution of primes, Acta Arithmetica, Volume 41, Issue 1, 1916, 119–196.