Ramanujan Summation for Pascal's Triangle

Authors

  • A. Dinesh Kumar Department of Mathematics, Khadir Mohideen College (Affiliated to Bharathidasan University), Adhirampattinam, Tamil Nadu, India https://orcid.org/0000-0001-6473-081X
  • R. Sivaraman Department of Mathematics, Dwaraka Doss Goverdhan Doss Vaishnav College, Chennai, India https://orcid.org/0000-0001-5989-4422

DOI:

https://doi.org/10.37256/cm.5120243150

Keywords:

Pascal’s triangle, Ramanujan summation, Pascal’s identity, hockey stick identity, Stirling’s numbers of first kind

Abstract

The concept of Pascal's triangle has fascinated not only professional mathematicians but also everyone interested in exploring science. Similarly, the idea of Ramanujan summation has made a revolution in mathematical research after it was introduced by Srinivasa Ramanujan. In this paper, we will provide the Ramanujan summation methods for numbers located in slant diagonals of Pascal's triangle and derive a generalized formula for such summations.

Downloads

Published

2024-02-29

How to Cite

1.
Dinesh Kumar A, Sivaraman R. Ramanujan Summation for Pascal’s Triangle. Contemp. Math. [Internet]. 2024 Feb. 29 [cited 2024 Dec. 21];5(1):817-25. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3150