A Gregory number is a number
 |
where 
is a rational number and 
is the inverse cotangent
in MathWorld's principal value convention. For
, this is 
, where 
is the inverse tangent.
At 
, 
. Gregory numbers arise
in the determination of Machin-like formulas.
Every Gregory number 
can be expressed uniquely as a finite linear
combination of 
s
with integer coefficients,
where the 
s
are Størmer numbers.
