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

1,2

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

Example

1.9771268308039343866983671752539756021366...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A281197 A373507 A199503 * A307715 A269547 A333345

Adjacent sequences: A242711 A242712 A242713 * A242715 A242716 A242717

Keyword

nonn,cons

Author

Jean-François Alcover, May 21 2014

Status

approved