A196877 Decimal expansion of Pi/2*(Pi^2/12 + (log(2))^2).

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

Offset: 1

Author

Seiichi Kirikami, Oct 07 2011

Keywords

• cons
• nonn

Comments

The value of the integral_{x=0..Pi/2} log(sin(x))^2 dx. The value of sqrt(Pi)/2*(d^2/da^2(gamma((a+1)/2)/gamma(a/2+1))) at a=0. - Seiichi Kirikami and Peter J. C. Moses, Oct 07 2011

Examples

			2.04662202447274064616964100817...
		

References

• I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 3.621.1

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• K. S. Kolbig, On the integral int_0^Pi/2 log^n cos x log^p sin x dx, Math. Comp. 40 (162) (1983) 565-570, r_{2,0}

Crossrefs

Cf. A002162, A019669, A072691, A173623, A196878.

Programs

Mathematica

RealDigits[N[Pi/2 (Pi^2/12 + Log[2]^2),150]][[1]]

PARI

Pi/2*(Pi^2/12+(log(2))^2) \\ Michel Marcus, Jan 13 2015

Formula

Equals A019669*(A072691 + A002162^2).

Equals Integral_{x=0..1} log(x)^2/sqrt(1-x^2) dx. - Amiram Eldar, May 27 2023