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A086281
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Decimal expansion of 4th Stieltjes constant gamma_4.
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12
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0, 0, 2, 3, 2, 5, 3, 7, 0, 0, 6, 5, 4, 6, 7, 3, 0, 0, 0, 5, 7, 4, 6, 8, 1, 7, 0, 1, 7, 7, 5, 2, 6, 0, 6, 8, 0, 0, 0, 9, 0, 4, 4, 6, 9, 4, 1, 3, 7, 8, 4, 8, 5, 0, 9, 9, 0, 7, 5, 8, 0, 4, 0, 9, 0, 7, 1, 2, 4, 8, 4, 1, 0, 0, 5, 3, 1, 5, 5, 2, 1, 9, 0, 0, 3, 0, 1, 6, 7, 8, 0, 5, 9, 0, 3, 9, 3, 0, 6, 3, 6, 0
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OFFSET
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0,3
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, p. 166.
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LINKS
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FORMULA
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Using the abbreviations a = log(z^2 + 1/4)/2, b = arctan(2*z) and c = cosh(Pi*z) then gamma_4 = -(Pi/5)*Integral_{0..infinity} (a^5-10*a^3*b^2+5*a*b^4)/c^2. The general case is for n>=0 (which includes Euler's gamma as gamma_0) gamma_n = (-Pi/ (n+1))*Integral_{0..infinity} sigma(n+1)/c^2, where sigma(n) = Sum_{k=0.. floor(n/2)}(-1)^k*binomial(n,2*k)*b^(2*k)*a^(n-2*k). - Peter Luschny, Apr 19 2018
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EXAMPLE
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0.0023253...
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MATHEMATICA
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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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