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Sqrt(e)

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The square root of
e
has the Maclaurin series expansion
where
n!!
is the double factorial.
2  e
is transcendental since
e
is transcendental.

Value

The decimal expansion of
2  e
is (A019774)

with continued fraction

giving the sequence (A058281
(n), n   ≥   0,
for
2  e
; A058281
(n), n   ≥   1,
for 1/(sqrt(e)-1)) with pattern
a (3k + 1) = 4k + 1, a(n) = 1
otherwise
{1, 1, 1, 1, 5, 1, 1, 9, 1, 1, 13, 1, 1, 17, 1, 1, 21, 1, 1, 25, 1, 1, 29, 1, 1, 33, 1, 1, 37, 1, 1, 41, 1, 1, 45, 1, 1, 49, 1, 1, 53, 1, 1, 57, 1, 1, 61, 1, 1, 65, 1, 1, 69, 1, 1, 73, 1, 1, 77, ...}

1/(sqrt(e)-1)

The decimal expansion of 1/(sqrt(e)-1) is (A113011)

with generalized continued fraction

See also