A series Formula for Pi found by Gregory and Leibniz,

It converges very slowly, but its convergence can be accelerated using certain transformations, in particular

where is the Riemann Zeta Function (Vardi 1991).

**References**

Vardi, I. *Computational Recreations in Mathematica.* Reading, MA: Addison-Wesley, pp. 157-158,
1991.

© 1996-9

1999-05-25