Apéry's Rational Approximation to His Constant

R. Apéry used a rapidly converging rational approximation to ζ(3) to prove its irrationality. Both numerator and denominator satisfy the same recurrence equation , with initial conditions , , , and . Approximately three decimal digits are gained with each degree. The notation means digits have been left out.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Many other rapidly convergent rational approximations to ζ(3) have been given since Apéry's original article.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.