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A016578
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Decimal expansion of log(3/2).
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9
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4, 0, 5, 4, 6, 5, 1, 0, 8, 1, 0, 8, 1, 6, 4, 3, 8, 1, 9, 7, 8, 0, 1, 3, 1, 1, 5, 4, 6, 4, 3, 4, 9, 1, 3, 6, 5, 7, 1, 9, 9, 0, 4, 2, 3, 4, 6, 2, 4, 9, 4, 1, 9, 7, 6, 1, 4, 0, 1, 4, 3, 2, 4, 1, 4, 4, 1, 0, 0, 6, 7, 1, 2, 4, 8, 9, 1, 4, 2, 5, 1, 2, 6, 7, 7, 5, 2, 4, 2, 7, 8, 1, 7, 3, 1, 3, 4, 0
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OFFSET
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0,1
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REFERENCES
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L. B. W. Jolley, Summation of Series, Dover (1961), eq (102), page 20.
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LINKS
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FORMULA
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Equals 1/2 - 1/(2*2^2) + 1/(3*2^3) - 1/(4*2^4) + ... [Jolley].
Equals 2 * arctanh(1/5).
Equals Integral_{x=0..oo} 1/(2*exp(x) + 1) dx. (End)
log(3/2) = 2*Sum_{n >= 1} 1/(n*P(n, 5)*P(n-1, 5)), where P(n, x) denotes the n-th Legendre polynomial. The first 10 terms of the series gives the approximation log(3/2) = 0.40546510810816438197(04...), correct to 20 decimal places. - Peter Bala, Mar 16 2024
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EXAMPLE
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0.4054651081081643819780131154643491365719904234624941976140143...
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MATHEMATICA
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PROG
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(PARI) default(realprecision, 20080); x=10*log(3/2); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b016578.txt", n, " ", d)); \\ Harry J. Smith, May 17 2009
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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