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Gregory Number

A number

t_x=\tan^{-1}({\textstyle{1\over x}})=\cot^{-1} x,

where $x$ is an Integer or Rational Number, $\tan^{-1}x$ is the Inverse Tangent, and $\cot^{-1}x$ is the Inverse Cotangent. Gregory numbers arise in the determination of Machin-Like Formulas. Every Gregory number $t_x$ can be expressed uniquely as a sum of $t_n$s where the $n$s are Størmer Numbers.


Conway, J. H. and Guy, R. K. ``Gregory's Numbers'' In The Book of Numbers. New York: Springer-Verlag, pp. 241-242, 1996.

© 1996-9 Eric W. Weisstein