2.7182818284590452353602874713…

The Powerful Power Series for e: Polynomial vanishing and the transcendence of e
  • Edward B. Burger
  • Robert Tubbs

Abstract

Here we will investigate several features of one of the most famous and important numbers in mathematics, namely, Leonhard Euler’s “e.” Our journey through this chapter sets the stage for much of what follows in our future explorations. To foreshadow the fundamental strategies to come, we open with Joseph Fourier’s 1815 clever proof of Euler’s result that e is irrational.

Keywords

Number Theory Rational Number Rational Approximation Previous Argument Power Series Expansion 
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Copyright information

© E.B. Burger and R. Tubbs 2004

Authors and Affiliations

  • Edward B. Burger
    • 1
  • Robert Tubbs
    • 2
  1. 1.Department of MathematicsWilliams CollegeWilliamstownUSA
  2. 2.Department of MathematicsUniversity of Colorado at BoulderBoulderUSA

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