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A340350 Decimal expansion of Integral_{x=0..Pi/2, y=0..Pi/2} log(1 + sin(x)^2*sin(y)^2) dy dx. 5
4, 9, 5, 3, 1, 6, 6, 1, 8, 6, 9, 2, 1, 2, 3, 3, 6, 4, 3, 0, 2, 9, 6, 5, 0, 4, 0, 4, 1, 1, 6, 1, 0, 4, 7, 5, 8, 8, 7, 1, 7, 8, 8, 4, 1, 7, 6, 7, 9, 7, 4, 5, 1, 8, 2, 4, 6, 4, 7, 4, 5, 9, 3, 4, 1, 1, 2, 3, 7, 7, 4, 0, 6, 1, 2, 4, 7, 1, 1, 3, 6, 1, 4, 3, 4, 5, 6, 5, 3, 5, 0, 3, 2, 6, 6, 3, 7, 5, 2, 8, 7, 7, 9, 2, 3, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..105.

FORMULA

Equals Pi * Integral_{x=0..Pi/2} log((1 + sqrt(1 + sin(x)^2))/2) dx.

Equals limit_{n->infinity} Pi^2 * (log(A340165(n)) / (2*n^2) - log(2)).

Equals limit_{n->infinity} Pi^2 * (log(A340167(n)) / (4*n^2) - log(2)).

EXAMPLE

0.49531661869212336430296504041161047588717884176797451824647459341123774...

MAPLE

evalf(Pi * Integrate(log((1 + sqrt(1 + sin(x)^2))/2), x = 0..Pi/2), 120);

MATHEMATICA

RealDigits[N[Pi*Integrate[Log[(1 + Sqrt[1 + Sin[x]^2])/2], {x, 0, Pi/2}], 100]][[1]]

PROG

(PARI) Pi * intnum(x = 0, Pi/2, log((1 + sqrt(1 + sin(x)^2))/2))

CROSSREFS

Cf. A097469, A340165, A340167, A340322, A340421, A340422.

Sequence in context: A121305 A200396 A011513 * A164818 A065796 A070434

Adjacent sequences:  A340347 A340348 A340349 * A340351 A340352 A340353

KEYWORD

nonn,cons

AUTHOR

Vaclav Kotesovec, Jan 05 2021

STATUS

approved

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Last modified October 5 23:01 EDT 2022. Contains 357261 sequences. (Running on oeis4.)