## 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.
MR 55\#9490.
Abstract:
dvi (3K),
pdf (82K),
ps (28K).

Paper:
pdf (455K).

Review by Daniel Shanks in
* Mathematics of Computation * 32 (1978), 311:
pdf (107K).

## Abstract

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
*P*/*Q* for
integers *P* and *Q*, then
|*Q*| > 10^{10000}.
## Comments

It is not known whether gamma or exp(gamma) is rational;
the lower bound on *Q* shows that neither is a
*small* rational.
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
Ramanujan
is described in Brent [139].

For a sequel which introduced some more efficient algorithms
and extended the computation, see
Brent and McMillan [49].

Go to next publication

Return to Richard Brent's index page