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

1,1

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

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}

Formula

Equals A019669*(A072691 + A002162^2).

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

Example

2.04662202447274064616964100817...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A342384 A192134 A322402 * A098123 A066659 A343468

Adjacent sequences: A196874 A196875 A196876 * A196878 A196879 A196880

Keyword

cons,nonn

Author

Seiichi Kirikami, Oct 07 2011

Status

approved