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A336266
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Decimal expansion of (3/16)*Pi.
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4
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5, 8, 9, 0, 4, 8, 6, 2, 2, 5, 4, 8, 0, 8, 6, 2, 3, 2, 2, 1, 1, 7, 4, 5, 6, 3, 4, 3, 6, 4, 9, 0, 6, 7, 9, 0, 7, 8, 6, 9, 6, 9, 2, 6, 2, 3, 8, 2, 8, 3, 2, 3, 4, 1, 4, 3, 2, 8, 0, 2, 1, 1, 1, 0, 5, 7, 7, 1, 5, 5, 7, 6, 1, 7, 8, 6, 6, 4, 1, 8, 7, 2, 4, 2, 7, 5, 6, 5
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OFFSET
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0,1
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COMMENTS
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Area of one egg of the "double egg" whose polar equation is r(t) = a * cos(t)^2 and a Cartesian equation is (x^2+y^2)^3 = a^2*x^4 is equal to (3/16)*Pi * a^2. See the curve at the Mathcurve link.
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REFERENCES
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L. Lorentzen and H. Waadeland, Continued Fractions with Applications, North-Holland 1992, p. 586.
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LINKS
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FORMULA
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Equals Integral_{t=0..Pi} (1/2) * cos(t)^4 * dt.
Equals Integral_{x=0..oo} 1/(x^2 + 1)^3 dx. - Amiram Eldar, Aug 13 2020
Equals 1/2 + Sum_{n >= 0} (-1)^n/(u(n)*u(-n)), where the polynomial u(n) = (2*n - 1)*(4*n^2 - 4*n + 3)/3 = A057813(n-1) has its zeros on the vertical line Re(z) = 1/2 in the complex plane. Cf. A336308.
Equals 1/2 + 1/(11 + 3/(12 + 15/(12 + 35/(12 + ... + (4*n^2 - 1)/(12 + ... ))))). See Lorentzen and Waadeland, p. 586, equation 4.7.10 with n = 2. (End)
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EXAMPLE
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0.58904862254808623221174563436490679078696926...
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MAPLE
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evalf(3*Pi/16, 140);
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MATHEMATICA
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RealDigits[3*Pi/16, 10, 100][[1]] (* Amiram Eldar, Jul 15 2020 *)
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PROG
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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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