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A359283
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Decimal expansion of Integral_{x = 1..oo} 1/x^(x^2) dx.
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4
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4, 6, 2, 3, 0, 3, 7, 1, 1, 5, 3, 7, 3, 2, 1, 0, 7, 7, 1, 8, 2, 0, 3, 9, 6, 2, 8, 5, 8, 8, 2, 7, 7, 4, 4, 0, 9, 6, 1, 0, 2, 6, 0, 3, 7, 0, 4, 8, 4, 0, 7, 5, 6, 2, 2, 7, 0, 1, 3, 0, 0, 6, 0, 2, 5, 6, 7, 8, 2, 3, 3, 7, 7, 0, 2, 4, 0, 9, 8, 4, 4, 7, 7, 3, 4, 1, 7, 5, 4, 6, 1, 0, 5, 4, 2, 3, 3, 8, 6, 1, 8
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OFFSET
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0,1
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COMMENTS
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For a, b nonnegative integers, the alternating divergent series Sum_{n >= 0} (-1)^n*(a*n + b)^n is Borel summable to Integral_{x = 1..oo} x^(a-b-1)/x^(x^a) dx.
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LINKS
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FORMULA
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Equals Integral_{x = 1..oo} 1/(2*x - 1)^x dx.
Equals the Borel sum of the alternating divergent series Sum_{n >= 0} (-1)^n*(2*n + 1)^n. Compare with the alternating convergent series Sum_{n >= 1} (-1)^(n+1)/(2*n - 1)^n = Integral_{x = 0..1} x^(x^2) dx. See A253299.
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EXAMPLE
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0.46230371153732107718203962858827744096102603704840...
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MAPLE
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evalf(int(1/x^(x^2), x = 1..infinity), 100);
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MATHEMATICA
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NIntegrate[1/x^(x^2), {x, 1, Infinity}, WorkingPrecision -> 105] // RealDigits // First
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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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