Stoneham's series

[ttw]

Stoneham has a few funny series. Here are two that converge to Sqrt(2) and Pi. These seem similar in pattern but one has a quadratic surd for a limit and the other a transcendental number.

Sqrt(2) = 2 * Prod (1-1/(4*d^2) taken over all d odd.

Pi= 4 * Prod( 1-1/d^2) taken over all d>1.

"Random Generators and Normal Numbers"
David H. Bailey and Richard E. Crandall
from
Experimental Mathematics, Vol. 11 (2002), No. 4