Gregory Number

A number

t_x=tan^(-1)(1/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 linear combination of t_ns where the ns are Størmer numbers.

See also

Machin-Like Formulas, Størmer Number

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References

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

Referenced on Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Gregory Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GregoryNumber.html

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