Computation of the regular continued fraction for Euler's constant
40. R. P. Brent,
Computation of the regular continued fraction for Euler's constant,
Mathematics of Computation 31 (1977), 771-777.
Review by Daniel Shanks in
Mathematics of Computation 32 (1978), 311:
We describe a computation,
using the MP package,
of the first 20,000 partial quotients in
the regular continued fraction for Euler's constant
gamma = 0.577...
and exp(gamma) = 1.781...
A preliminary step was the calculation
of gamma and exp(gamma) to 20,700D.
It follows from the continued
fractions that, if gamma or exp(gamma) is of the form
integers P and Q, then
|Q| > 1010000.
It is not known whether gamma or exp(gamma) is rational;
the lower bound on Q shows that neither is a
The computation of gamma improved on an earlier
(and only partially correct)
result of Beyer and Waterman
[Mathematics of Computation 28 (1974), 599-604].
An interesting connection with the work of
is described in Brent .
For a sequel which introduced some more efficient algorithms
and extended the computation, see
Brent and McMillan .
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