A194655 Decimal expansion of Pi*(Pi^2*zeta(3) + 6*zeta(5))/8.

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

Offset

1,1

Comments

The absolute value of Integral_{x=0..Pi/2} x^2*(log(2*cos(x)))^3 dx.

The absolute value of d^3/db^3(d^2/da^2(Integral_{x=0..Pi/2} cos(ax)*(2*cos(x))^b dx))).

The absolute value of m=2 and n=3 of (Pi/2)*(d^n/db^n(d^m/da^m(gamma(b+1)/gamma((b+a)/2+1)/gamma((b-a)/2+1)))). [Seiichi Kirikami and Peter J. C. Moses]

References

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 3.631.9

Links

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

Formula

Equals A000796*(A002388*A002117 + 6*A013663)/8.

Example

Equals 7.1021170790001686158...

Mathematica

RealDigits[ N[Pi (Pi^2*Zeta(3)+6*Zeta(5))/8, 150]][[1]]

Crossrefs

Cf. A152584, A193712, A193713, A194655.

Sequence in context: A223855 A289481 A229819 * A197037 A256778 A218620

Adjacent sequences: A194652 A194653 A194654 * A194656 A194657 A194658

Keyword

cons,nonn

Author

Seiichi Kirikami, Aug 31 2011

Status

approved