In
mathematics, a Gregory number, named after
James Gregory, is a
real number
In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every ...
of the form:
:
where ''x'' is any rational number greater or equal to 1. Considering the
power series
In mathematics, a power series (in one variable) is an infinite series of the form
\sum_^\infty a_n \left(x - c\right)^n = a_0 + a_1 (x - c) + a_2 (x - c)^2 + \dots
where ''an'' represents the coefficient of the ''n''th term and ''c'' is a con ...
expansion for
arctangent, we have
:
Setting ''x'' = 1 gives the well-known
Leibniz formula for pi. Thus, in particular,
:
is a Gregory number.
Properties
*
*
See also
*
Størmer number In mathematics, a Størmer number or arc-cotangent irreducible number is a positive integer n for which the greatest prime factor of n^2+1 is greater than or equal to 2n. They are named after Carl Størmer.
Sequence
The first few Størmer numbers ...
References
Sets of real numbers
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