A340421 - OEIS

A340421

Decimal expansion of Integral_{x=0..Pi/2, y=0..Pi/2} log(1 + sin(x)^2 + sin(y)^2) dy dx.

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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..105.

FORMULA

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

Equals limit_{n->infinity} Pi^2 * (log(A340396(n))/n^2 - log(2)) / 4.

EXAMPLE

1.627008991085721315763766677017604437985734719035793082916212355323520769...

MATHEMATICA

RealDigits[N[-Pi^2*(Log[2] + Log[Sqrt[2] - 1]/2) + Pi*Integrate[Log[1 + Sqrt[1 + 1/(1 + Sin[x]^2)]], {x, 0, Pi/2}], 120], 10, 110][[1]]