A242714 Decimal expansion of C_6, a constant related to sharp inequalities for the product of 6 polynomials, which was introduced by David Boyd.

1, 9, 7, 7, 1, 2, 6, 8, 3, 0, 8, 0, 3, 9, 3, 4, 3, 8, 6, 6, 9, 8, 3, 6, 7, 1, 7, 5, 2, 5, 3, 9, 7, 5, 6, 0, 2, 1, 3, 6, 6, 0, 4, 9, 7, 2, 7, 9, 6, 5, 1, 1, 8, 1, 0, 7, 2, 4, 4, 4, 5, 7, 8, 5, 7, 4, 3, 9, 7, 0, 0, 8, 9, 6, 8, 0, 9, 9, 7, 8, 2, 2, 9, 8, 9, 9, 1, 9, 0, 0, 2, 7, 5, 0, 5, 0, 2, 5, 0, 7

Offset: 1

Author

Jean-François Alcover, May 21 2014

Keywords

• nonn
• cons

Examples

			1.9771268308039343866983671752539756021366...
		

References

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

Links

• David W. Boyd, Sharp inequalities for the product of polynomials
• Eric Weisstein's MathWorld, Clausen's Integral

Crossrefs

Cf. A130834 (C_2), A242711 (C_3), A242712 (C_4), A242713 (C_5).

Programs

Mathematica

Clausen2[x_] := Im[PolyLog[2, Exp[x*I]]]; c[m_] := Exp[m/Pi*Clausen2[Pi - Pi/m]]; RealDigits[c[6], 10, 100] // First

PARI

exp(6*imag(polylog(2, exp(5*I*Pi/6)))/Pi) \\ Charles R Greathouse IV, Jul 15 2014

Formula

exp(6/Pi*Clausen2(Pi - Pi/6)), where Clausen2 is Clausen's Integral.