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A019683
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Decimal expansion of Pi/16.
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10
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1, 9, 6, 3, 4, 9, 5, 4, 0, 8, 4, 9, 3, 6, 2, 0, 7, 7, 4, 0, 3, 9, 1, 5, 2, 1, 1, 4, 5, 4, 9, 6, 8, 9, 3, 0, 2, 6, 2, 3, 2, 3, 0, 8, 7, 4, 6, 0, 9, 4, 4, 1, 1, 3, 8, 1, 0, 9, 3, 4, 0, 3, 7, 0, 1, 9, 2, 3, 8, 5, 2, 5, 3, 9, 2, 8, 8, 8, 0, 6, 2, 4, 1, 4, 2, 5, 2, 1, 7, 6, 5, 8, 3, 8, 8, 2, 3, 1, 6
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OFFSET
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0,2
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LINKS
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FORMULA
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Equals Integral_{x = 0..1} x^2*sqrt(1 - x^2) dx = Integral_{x = 0..1} x^3*sqrt(1 - x^8) dx.
Equals Integral_{x = 0..inf} x^2/(1 + x^2)^3 dx. (End)
Equals Sum_{k>=1} sin(k)^3 * cos(k)/k.
Equals Sum_{k>=1} sin(k)^3 * cos(k)^2/k.
Equals Sum_{k>=1} (-1)^(k+1) * sin((2*k-1)/4)/(2*k-1)^2. (End)
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EXAMPLE
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MATHEMATICA
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PROG
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(PARI) default(realprecision, 100); Pi/16 \\ G. C. Greubel, Aug 26 2019
(Magma) R:= RealField(100); Pi(R)/16; // G. C. Greubel, Aug 26 2019
(Sage) numerical_approx(pi/16, digits=100) # G. C. Greubel, Aug 26 2019
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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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