A193713 Decimal expansion of 11*Pi^5/1440.

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

Offset: 1

Author

Seiichi Kirikami, Aug 31 2011

Keywords

• cons
• easy
• nonn

Comments

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

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

The value of Pi/2*(d^2/db^2(d^2/da^2(gamma(b+1)/gamma((b+a)/2+1)/gamma((b-a)/2+1)))) at a=0 and b=0. [Seiichi Kirikami and Peter J. C. Moses]

Examples

			2.3376503698875666568...
		

References

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

Links

• Jonathan Sondow and Eric W. Weisstein Harmonic Number (22)
• Index entries for transcendental numbers

Crossrefs

Cf. A152584, A193712, A194655.

Programs

Mathematica

RealDigits[ N[11 Pi^5/1440, 150]][[1]]

Formula

Equals 11*A092731/1440.