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