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A093828
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Decimal expansion of (3*Pi)/8.
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6
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1, 1, 7, 8, 0, 9, 7, 2, 4, 5, 0, 9, 6, 1, 7, 2, 4, 6, 4, 4, 2, 3, 4, 9, 1, 2, 6, 8, 7, 2, 9, 8, 1, 3, 5, 8, 1, 5, 7, 3, 9, 3, 8, 5, 2, 4, 7, 6, 5, 6, 6, 4, 6, 8, 2, 8, 6, 5, 6, 0, 4, 2, 2, 2, 1, 1, 5, 4, 3, 1, 1, 5, 2, 3, 5, 7, 3, 2, 8, 3, 7, 4, 4, 8, 5, 5, 1, 3, 0, 5, 9, 5, 0, 3, 2, 9, 3, 9, 0, 0, 4, 9
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OFFSET
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1,3
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COMMENTS
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Area of an astroid with a = 1.
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LINKS
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Eric Weisstein's World of Mathematics, Astroid.
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FORMULA
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Equals arctan(1 + sqrt(2)).
Equals Integral_{x=0..1} x^(3/2)/sqrt(1-x) dx. (End)
Equals Sum_{k>=1} sin(k*Pi/4)/k. - Amiram Eldar, May 30 2021
3*Pi/8 = Sum_{n >= 1} n*(n+1)*2^(n+1)/binomial(2*n+6,n+3) (apply Euler's series transformation to the series representation Pi = 384*Sum_{n >= 1} (-1)^(n+1)*n^2/((4*n^2 - 1)*(4*n^2 - 9)*(4*n^2 - 25)) ). - Peter Bala, Dec 08 2021
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EXAMPLE
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1.1780972450961724644234912687298135815739385247656646...
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MAPLE
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MATHEMATICA
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RealDigits[3*Pi/8, 10, 105][[1]] (* G. C. Greubel, Aug 11 2019 *)
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PROG
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(PARI) { default(realprecision, 20080); x=3*Pi/8; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b093828.txt", n, " ", d)); } \\ Harry J. Smith, Jun 18 2009
(Magma) SetDefaultRealField(RealField(110)); R:= RealField(); 3*Pi(R)/8; // G. C. Greubel, Aug 11 2019
(Sage) numerical_approx(3*pi/8, digits=110) # G. C. Greubel, Aug 11 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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