|
%I #7 Jul 15 2014 10:01:38
%S 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,
%T 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,
%U 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
%N Decimal expansion of C_6, a constant related to sharp inequalities for the product of 6 polynomials, which was introduced by David Boyd.
%D S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 3.10 p. 233.
%H David W. Boyd, <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.122.861&rep=rep1&type=pdf">Sharp inequalities for the product of polynomials</a>
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/ClausensIntegral.html">Clausen's Integral</a>
%F exp(6/Pi*Clausen2(Pi - Pi/6)), where Clausen2 is Clausen's Integral.
%e 1.9771268308039343866983671752539756021366...
%t Clausen2[x_] := Im[PolyLog[2, Exp[x*I]]]; c[m_] := Exp[m/Pi*Clausen2[Pi - Pi/m]]; RealDigits[c[6], 10, 100] // First
%o (PARI) exp(6*imag(polylog(2, exp(5*I*Pi/6)))/Pi) \\ _Charles R Greathouse IV_, Jul 15 2014
%Y Cf. A130834 (C_2), A242711 (C_3), A242712 (C_4), A242713 (C_5).
%K nonn,cons
%O 1,2
%A _Jean-François Alcover_, May 21 2014
|
