A242711 Decimal expansion of C_3, a constant related to sharp inequalities for the product of 3 polynomials, which was introduced by David Boyd.

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

Offset

1,2

References

Steven 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-François Alcover, May 21 2014

Status

approved