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A244928
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Decimal expansion of Ti_2(2-sqrt(3)), where Ti_2 is the inverse tangent integral function.
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2
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2, 6, 5, 8, 6, 4, 9, 5, 8, 2, 7, 9, 3, 0, 6, 9, 8, 2, 6, 9, 1, 8, 7, 5, 0, 8, 6, 3, 9, 7, 1, 2, 0, 6, 8, 7, 6, 4, 2, 7, 8, 3, 8, 2, 3, 9, 7, 5, 1, 3, 8, 9, 9, 9, 3, 8, 0, 5, 9, 7, 4, 1, 5, 3, 2, 8, 5, 7, 4, 3, 9, 5, 1, 3, 0, 2, 7, 7, 1, 1, 4, 0, 5, 4, 4, 1, 1, 4, 0, 7, 0, 3, 2, 0, 5, 7, 7, 1, 7, 4, 0, 4, 5, 7, 1
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OFFSET
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0,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.7.6 Inverse Tangent Integral, p. 57.
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LINKS
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FORMULA
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2/3*G + Pi/12*log(2-Sqrt(3)), where G is Catalan's number.
Also equals i/2*(polylog(2, -i*(2-sqrt(3))) - polylog(2, i*(2-sqrt(3)))), with i = sqrt(-1).
Equals 3F2(1/2,1,1; 3/2,3/2 ; 1/4)/4 [Krupnikov] - R. J. Mathar, May 13 2024
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EXAMPLE
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0.26586495827930698269187508639712068764278382397513899938059741532857439513...
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MATHEMATICA
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2/3*Catalan + Pi/12*Log[2 - Sqrt[3]] // RealDigits[#, 10, 105]& // First
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PROG
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(PARI) default(realprecision, 100); (2/3)*Catalan + Pi/12*log(2 - sqrt(3)) \\ G. C. Greubel, Aug 25 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); (2/3)*Catalan(R) + Pi(R)/12*Log(2 - Sqrt(3)); // G. C. Greubel, Aug 25 2018
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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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