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A trigonometric approach to an identity by Ramanujan

C. Vignat

Abstract

An identity by Ramanujan is expressed using polar coordinates, so that its proof reduces to the verification of an elementary trigonometric identity. This approach produces a few variations on Ramanujan's original identity.

A trigonometric approach to an identity by Ramanujan

Abstract

An identity by Ramanujan is expressed using polar coordinates, so that its proof reduces to the verification of an elementary trigonometric identity. This approach produces a few variations on Ramanujan's original identity.
Paper Structure (6 sections, 7 theorems, 45 equations)

This paper contains 6 sections, 7 theorems, 45 equations.

Table of Contents

  1. Introduction
  2. A trigonometric approach
  3. Generalizations
  4. Proofs of Lemmas 1 and 2
  5. Proof of Lemma \ref{['lemma1']}
  6. A trigonometric identity

Key Result

Proposition 1

Let $a,b,c$ and $d$ be any numbers such that $ad=bc.$ Then

Theorems & Definitions (8)

  • Proposition
  • Lemma 1
  • Lemma 2
  • Proposition
  • Proposition
  • Proposition
  • Proposition
  • proof