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A244928 Decimal expansion of Ti_2(2-sqrt(3)), where Ti_2 is the inverse tangent integral function. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.7.6 Inverse Tangent Integral, p. 57.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

Eric Weisstein's MathWorld, Inverse Tangent Integral

Eric Weisstein's MathWorld, Polylogarithm

FORMULA

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).

EXAMPLE

0.26586495827930698269187508639712068764278382397513899938059741532857439513...

MATHEMATICA

2/3*Catalan + Pi/12*Log[2 - Sqrt[3]] // RealDigits[#, 10, 105]& // First

PROG

(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

CROSSREFS

Cf. A006752, A244929.

Sequence in context: A199159 A175293 A021083 * A319016 A262096 A011043

Adjacent sequences:  A244925 A244926 A244927 * A244929 A244930 A244931

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Jul 08 2014

STATUS

approved

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Last modified December 1 14:10 EST 2021. Contains 349430 sequences. (Running on oeis4.)