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A187832
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Decimal expansion of integral from 1/2 to 1 of (1-x)/x dx.
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6
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1, 9, 3, 1, 4, 7, 1, 8, 0, 5, 5, 9, 9, 4, 5, 3, 0, 9, 4, 1, 7, 2, 3, 2, 1, 2, 1, 4, 5, 8, 1, 7, 6, 5, 6, 8, 0, 7, 5, 5, 0, 0, 1, 3, 4, 3, 6, 0, 2, 5, 5, 2, 5, 4, 1, 2, 0, 6, 8, 0, 0, 0, 9, 4, 9, 3, 3, 9, 3, 6, 2, 1, 9, 6, 9, 6, 9, 4, 7, 1, 5, 6, 0, 5, 8, 6, 3, 3, 2, 6, 9, 9, 6, 4, 1, 8, 6, 8, 7, 5, 4, 2, 0, 0, 1
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OFFSET
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0,2
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COMMENTS
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Replacing 1/2 with any other number 0 < t < 1, the value of the integral is t - 1 - log(t).
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REFERENCES
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J.-M. Monier, Cours, Analyse, Tome 4, 2ème année, MP.PSI.PC.PT, Dunod, 1997, Exercice 4.3.14 pages 53 and 367.
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LINKS
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FORMULA
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Equals log(2) - 1/2 = A002162 - 1/2.
Equals Sum_{k>=1} 1/((2k-1)*(2k)*(2k+1)). - Bruno Berselli, Mar 16 2014
Equals Sum_{k>=0} (-1)^k/(k+3).
Equals Sum_{k>=2} 1/(k * 2^k).
Equals Sum_{k>=2} 1/(4*k^2 - 2*k).
Equals Sum_{k>=2} (zeta(k) - 1)/2^k.
Equals Sum_{k>=1} zeta(2*k + 1)/2^(2*k + 1). (End)
Equals Sum_{k>=1} (S(k) - log(2)) when S(k) = Sum_{m=1..k} (-1)^(m+1) / m.
Equals Integral_{x=0..1} x/(1+x)^2 dx. (End)
Equals Sum_{k,m>=1} (-1)^(k+m)/(k+m). - Amiram Eldar, Jun 09 2022
Equals Integral_{x = 0..1} Integral_{y = 0..1} x*y/(x + y)^2 dy dx. - Peter Bala, Dec 12 2022
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EXAMPLE
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0.193147180559945309417232121458176568075500134360255254120680009493393621969...
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MAPLE
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MATHEMATICA
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RealDigits[Log[2] - 1/2, 10, 111][[1]]
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PROG
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CROSSREFS
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Apart from the first digit the same as A002162.
Cf. A239354: Sum_{k>=1} 1/((2k)*(2k+1)*(2k+2)).
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KEYWORD
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AUTHOR
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STATUS
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approved
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