A233090 Decimal expansion of Sum_{n>=1} (-1)^(n-1)*H(n)/n^2, where H(n) is the n-th harmonic number.
7, 5, 1, 2, 8, 5, 5, 6, 4, 4, 7, 4, 7, 4, 6, 4, 2, 8, 3, 7, 4, 8, 3, 6, 3, 5, 0, 9, 4, 4, 6, 5, 6, 2, 4, 4, 2, 2, 8, 1, 1, 6, 4, 3, 2, 7, 1, 2, 8, 1, 1, 8, 0, 1, 1, 2, 0, 1, 6, 9, 7, 2, 2, 0, 8, 8, 6, 4, 8, 8, 7, 8, 6, 1, 6, 4, 4, 5, 6, 8, 1, 3, 6, 6, 5, 3, 4, 9, 2, 1, 0, 0, 5, 8, 3, 4, 5, 3, 6, 3
Offset: 0
Examples
0.7512855644747464283748363509446562442281164327128118011201697220886...
References
- Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.3, p. 43.
Links
- R. Barbieri, J. A. Mignaco, and E. Remiddi, Electron form factors up to fourth order. I., Il Nuovo Cim. 11A (4) (1972) 824-864, table II (13)
- Philippe Flajolet and Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998), page 32.
- Paul J. Nahin, Inside interesting integrals, Undergrad. Lecture Notes in Physics, Springer (2020), (C5.15)
- Michael I. Shamos, A catalog of the real numbers, (2007). See p. 561.
Crossrefs
Programs
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Mathematica
RealDigits[ 5*Zeta[3]/8, 10, 100] // First
Formula
Equals 5*zeta(3)/8.
Equals -Integral_{x=0..1} (log(1+x)*log(1-x)/x)*dx. - Amiram Eldar, May 06 2023
Equals Sum_{m>=1} Sum_{n>=1} (-1)^(m-1)/(m*n*(m + n)) (see Finch). - Stefano Spezia, Nov 02 2024