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A242711 Decimal expansion of C_3, a constant related to sharp inequalities for the product of 3 polynomials, which was introduced by David Boyd. 3
1, 9, 0, 8, 1, 4, 5, 6, 2, 6, 8, 1, 2, 7, 8, 5, 6, 7, 2, 4, 1, 5, 7, 5, 2, 6, 9, 4, 8, 8, 8, 4, 3, 9, 6, 0, 8, 2, 8, 1, 0, 5, 7, 8, 6, 5, 5, 7, 2, 2, 3, 9, 8, 1, 8, 7, 9, 5, 0, 5, 1, 7, 8, 7, 9, 8, 4, 0, 8, 7, 1, 9, 1, 5, 3, 4, 6, 2, 8, 6, 4, 9, 2, 0, 7, 3, 3, 1, 9, 1, 7, 4, 0, 4, 3, 1, 1, 2, 0, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 3.10 p. 233.

LINKS

Table of n, a(n) for n=1..100.

David W. Boyd, Sharp inequalities for the product of polynomials

Eric Weisstein's MathWorld, Clausen's Integral

FORMULA

exp(3/Pi*Clausen2(Pi - Pi/3)), where Clausen2 is Clausen's Integral.

EXAMPLE

1.908145626812785672415752694888439608281...

MATHEMATICA

Clausen2[x_] := Im[PolyLog[2, Exp[x*I]]]; c[m_] := Exp[m/Pi*Clausen2[Pi - Pi/m]]; RealDigits[c[3], 10, 100] // First

PROG

(PARI) exp(3*imag(polylog(2, exp(2*I*Pi/3)))/Pi) \\ Charles R Greathouse IV, Jul 14 2014

CROSSREFS

Cf. A130834 (C_2), A242712 (C_4), A242713 (C_5), A242714 (C_6).

Sequence in context: A202955 A019820 A019985 * A178229 A021995 A013677

Adjacent sequences:  A242708 A242709 A242710 * A242712 A242713 A242714

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, May 21 2014

STATUS

approved

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Last modified August 18 01:19 EDT 2019. Contains 326059 sequences. (Running on oeis4.)