Apéry's Rational Approximation to His Constant

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

R. Apéry used a rapidly converging rational approximation to 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.

Contributed by: Oleksandr Pavlyk (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Many other rapidly convergent rational approximations to have been given since the original article of Apéry.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send