Search engine for discovering works of Art, research articles, and books related to Art and Culture
ShareThis
Javascript must be enabled to continue!

On an identity of Ramanujan

View through CrossRef
Proofs published so far in articles and books, of the Ramanujan identity presented in this note, which depend on Euler products, are essentially the same as Ramanujan's original proof. In contrast, the proof given here is short and independent of the use of Euler products.
Centre pour la Communication Scientifique Directe (CCSD)
Title: On an identity of Ramanujan
Description:
Proofs published so far in articles and books, of the Ramanujan identity presented in this note, which depend on Euler products, are essentially the same as Ramanujan's original proof.
In contrast, the proof given here is short and independent of the use of Euler products.

Related Results

Dual Ramanujan-Fourier series
Dual Ramanujan-Fourier series
Let cq(n) be the Ramanujan sums. Many results concerning Ramanujan-Fourier series f (n) = ∞ q=1 aqcq(n) are obtained by many mathematicians. In this paper we study series of the fo...
New and explicit constructions of unbalanced Ramanujan bipartite graphs
New and explicit constructions of unbalanced Ramanujan bipartite graphs
AbstractThe objectives of this article are threefold. Firstly, we present for the first time explicit constructions of an infinite family of unbalanced Ramanujan bigraphs. Secondly...
Zheng Xiaoyun`s Theory of Cultural Identity
Zheng Xiaoyun`s Theory of Cultural Identity
This article is an analysis of the theory of cultural identity by Zheng Xiaoyun, a distinguished Chinese philosopher. His theory of cultural identity presented here gives a new per...
A note on the zeros of approximations of the Ramanujan $$\Xi $$-function
A note on the zeros of approximations of the Ramanujan $$\Xi $$-function
AbstractIn this paper we review the study of the distribution of the zeros of certain approximations for the Ramanujan $$\Xi $$ Ξ -function given ...
Ramanujan Summation for Pascal’s Triangle
Ramanujan Summation for Pascal’s Triangle
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 h...
Some New Ramanujan's Modular Equations of Degree 15
Some New Ramanujan's Modular Equations of Degree 15
Abstract Ramanujan in his notebook recorded two modular equations involving multiplier with moduli of degrees (1,7) and (1,23). In this paper, we find some new Ramanujan's ...
A.K. Ramanujan: A Poet of Different Cultures and Languages
A.K. Ramanujan: A Poet of Different Cultures and Languages
The paper explores the impact of different cultures and languages in the poetic writings of A. K. Ramanujan. He has a full command over Indian culture, scriptures and rituals. Tami...

Back to Top