2 added 1 characters in body

There are marvelous approximations to \pi based on modular functions related to the Hilbert Class 1 Heegner numbers and Class 2 numbers like 58. The numbers 29 = 58/2 and 145 = 5*29 are interesting in your approximation. For example:

e^{\pi\sqrt{58}}

e^{\pi \sqrt{58}} \approx (5+\sqrt{29})^12/64 + 24.

But I don't think your question corresponds to these modular approximations You can find articles describing the modular function approximations at http://sites.google.com/site/tpiezas/ramanujan.

1

There are marvelous approximations to \pi based on modular functions related to the Hilbert Class 1 Heegner numbers and Class 2 numbers like 58. The numbers 29 = 58/2 and 145 = 5*29 are interesting in your approximation. For example:

e^{\pi\sqrt{58}} \approx (5+\sqrt{29})^12/64 + 24.

But I don't think your question corresponds to these modular approximations You can find articles describing the modular function approximations at http://sites.google.com/site/tpiezas/ramanujan.