A369884 Decimal expansion of - Integral_{x=0..1} log(1 - x)/(x^2 + x) dx.
1, 0, 6, 2, 6, 9, 3, 5, 4, 0, 3, 8, 3, 2, 1, 3, 9, 3, 0, 5, 6, 9, 7, 5, 8, 8, 4, 6, 4, 8, 6, 3, 4, 5, 0, 8, 0, 4, 7, 4, 7, 5, 1, 4, 2, 6, 4, 0, 0, 6, 7, 2, 0, 1, 2, 3, 0, 1, 2, 1, 1, 1, 8, 1, 4, 9, 6, 8, 3, 6, 4, 2, 6, 3, 3, 1, 5, 1, 7, 6, 7, 3, 0, 1, 6, 7, 8, 8, 5, 8, 2, 0, 3, 1, 8, 4, 2, 8, 4, 8, 1, 1, 8, 3, 5, 9, 9
Offset: 1
Examples
1.062693540383213930569758846486345080474751426...
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 I (8).
- Michael Ian Shamos, A catalog of the real numbers (2011), p. 110.
- Eric Weisstein's World of Mathematics, Harmonic Number
- Wikipedia, Harmonic number.
Programs
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Mathematica
RealDigits[Pi^2/12 + Log[2]^2/2, 10, 120][[1]] (* Amiram Eldar, Feb 04 2024 *)
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PARI
- intnum(x=0,1,log(1-x)/(x^2+x))
Formula
Equals - Integral_{x=0..1} log(1 - x)/(x^2 + x) dx.
Equals Pi^2/12 + log(2)^2/2 [Shamos].
Equals Sum_{k=>1} H(k)^2/2^(k + 1), where H(k) is the k-th Harmonic number [Shamos].
Equals (Pi^2/6 + log(2)^2)/2 = A348373/2