A377645 Decimal expansion of 2*Pi^2*log(2) - 7*zeta(3).

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

Offset: 1

Author

Stefano Spezia, Nov 03 2024

Keywords

• nonn
• cons

Examples

			5.26777860559707309189679117732804220724465404999...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.5, p. 46.

Links

• Michael I. Shamos, A catalog of the real numbers, (2007). See p. 305.

Crossrefs

Cf. A002117, A002162, A002388, A016627, A164102.

Programs

Mathematica

RealDigits[2Pi^2Log[2]-7Zeta[3],10,100][[1]]

Formula

Equals -4*Integral_{x=0..Pi} x*log(sin(x/2)) dx = 8*Integral_{x=0..1} arcsin(x)^2/x dx = 8*Integral_{x=0..Pi/2} x^2*cot(x) dx (see Finch).

Equals Integral_{x=0..Pi} x^2*sin(x)/(1 - cos(x)) dx (see Shamos).