A336453 Decimal expansion of -Integral_{x=0..Infinity} log(x^2 + 1/4)/cosh(Pi*x)^2.

3, 6, 7, 4, 6, 6, 9, 0, 5, 1, 9, 6, 6, 1, 5, 9, 6, 1, 5, 1, 8, 5, 6, 8, 9, 3, 6, 2, 8, 7, 5, 1, 2, 3, 6, 5, 6, 5, 4, 5, 1, 7, 1, 2, 2, 2, 4, 2, 5, 6, 4, 8, 4, 9, 4, 4, 4, 3, 4, 8, 8, 3, 3, 4, 9, 8, 2, 5, 1, 2, 7, 7, 3, 9, 8, 4, 7, 2, 2, 8, 2, 5, 1, 6, 9, 3, 8, 4

Offset

0,1

Comments

Let c be the constant defined in the Name. It is unknown if the Euler constant gamma is transcendental. But if c is transcendental and c - Pi is not transcendental, then gamma is transcendental. (To see this note that c*Pi/2 = gamma.)

Links

Table of n, a(n) for n=0..87.

Example

0.36746690519661596151856893628751236565451712224256484944434883...

Maple

Digits := 100: lambda := (-int(log(x^2+1/4)/cosh(Pi*x)^2, x=0..infinity)):
evalf(lambda, 100)*10^90: ListTools:-Reverse(convert(floor(%), base, 10));

Crossrefs

Cf. A001620, A000796.

Sequence in context: A198457 A264921 A098990 * A162195 A117361 A228787

Adjacent sequences: A336450 A336451 A336452 * A336454 A336455 A336456

Keyword

nonn,cons

Author

Peter Luschny, Jul 22 2020

Status

approved