Special affine group

In mathematics, a Gregory number, named after James Gregory, is a real number of the form:

$G_{x}=\sum _{i=0}^{\infty }(-1)^{i}{\frac {1}{(2i+1)x^{2i+1}}}$

where x is any rational number greater or equal to 1. Considering the power series expansion for arctangent, we have

$G_{x}=\arctan {\frac {1}{x}}.$

Setting x = 1 gives the well-known Leibniz formula for pi.

See also

• Størmer number