Machin's Formula

Machin's formula is given by

There are a whole class of Machin-like formulas with various numbers of terms (although only four such formulas with only two terms). The properties of these formulas are intimately connected with cotangent identities.

REFERENCES:

Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A K Peters, p. 105, 2003.

Gourdon, X. and Sebah, P. "Collection of Series for ." http://numbers.computation.free.fr/Constants/Pi/piSeries.html.