The series for the inverse
tangent ,
Plugging in Gregory's formula
This series is intimately connected with the number of representations of Gauss's
circle problem (Hilbert and Cohn-Vossen 1999, pp. 27-39).
See also Gauss's Circle Problem ,
Gregory Series ,
Inverse
Tangent ,
Pi Formulas ,
Sum
of Squares Function
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References Hilbert, D. and Cohn-Vossen, S. Geometry and the Imagination. Wells,
D. The
Penguin Dictionary of Curious and Interesting Numbers. Referenced on Wolfram|Alpha Leibniz Series
Cite this as:
Weisstein, Eric W. "Leibniz Series." From
MathWorld https://mathworld.wolfram.com/LeibnizSeries.html
Subject classifications
gives Gregory's formula
by 
squares 
, and also with Gauss's
circle problem (Hilbert and Cohn-Vossen 1999, pp. 27-39).
