

A369884


Decimal expansion of  Integral_{x=0..1} log(1  x)/(x^2 + x) dx.


0



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
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OFFSET

1,3


LINKS



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 kth Harmonic number [Shamos].
Equals (Pi^2/6 + log(2)^2)/2 = A348373/2


EXAMPLE

1.062693540383213930569758846486345080474751426...


MATHEMATICA

RealDigits[Pi^2/12 + Log[2]^2/2, 10, 120][[1]] (* Amiram Eldar, Feb 04 2024 *)


PROG

(PARI)  intnum(x=0, 1, log(1x)/(x^2+x))


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



