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A sequence of elementary integrals related to integrals studied by Glaisher that contain trigonometric and hyperbolic functions

Martin Nicholson

Abstract

We generalize several integrals studied by Glaisher. These ideas are then applied to obtain an analog of an integral due to Ismail and Valent.

A sequence of elementary integrals related to integrals studied by Glaisher that contain trigonometric and hyperbolic functions

Abstract

We generalize several integrals studied by Glaisher. These ideas are then applied to obtain an analog of an integral due to Ismail and Valent.

Paper Structure

This paper contains 7 sections, 9 theorems, 78 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem \ref{['th1']}
  3. Proof of Theorem \ref{['th2']}
  4. Proof of Theorem \ref{['th3']}
  5. Proof of Theorem \ref{['th4']}
  6. Discussion
  7. Some open questions

Key Result

Theorem 1

Let $n$ be an odd integer, then

Theorems & Definitions (9)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Lemma 5
  • Lemma 6
  • Lemma 7
  • Lemma 8
  • Lemma 9