Gregory number

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In mathematics, a Gregory number, named after James Gregory, is a real number of the form:[1]

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

Setting x = 1 gives the well-known Leibniz formula for pi. Thus, in particular,

is a Gregory number.


See also[edit]


  1. ^ Conway, John H.; R. K. Guy (1996). The Book of Numbers. New York: Copernicus Press. pp. 241–243.