Variations on a theme of Apéry

Abstract

Apéry's remarkable discovery of rapidly converging continued fractions with small coefficients for $\hat{I}\P (2)$ and $\hat{I}\P (3)$ has led to a flurry of important activity in an incredible variety of different directions. Our purpose is to show that modifications of Apéry's continued fractions can give interesting results including new rapidly convergent continued fractions for certain interesting constants.

16 pages