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%I A242711 #10 Aug 06 2024 06:58:12
%S A242711 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,
%T A242711 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,
%U A242711 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
%N A242711 Decimal expansion of C_3, a constant related to sharp inequalities for the product of 3 polynomials, which was introduced by David Boyd.
%D A242711 S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 3.10 p. 233.
%H A242711 David W. Boyd, <a href="https://citeseerx.ist.psu.edu/pdf/522373ad9d2ff1a77a4054e6c28d8da3df682e5d">Sharp inequalities for the product of polynomials</a>
%H A242711 Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/ClausensIntegral.html">Clausen's Integral</a>
%F A242711 exp(3/Pi*Clausen2(Pi - Pi/3)), where Clausen2 is Clausen's Integral.
%e A242711 1.908145626812785672415752694888439608281...
%t A242711 Clausen2[x_] := Im[PolyLog[2, Exp[x*I]]]; c[m_] := Exp[m/Pi*Clausen2[Pi - Pi/m]]; RealDigits[c[3], 10, 100] // First
%o A242711 (PARI) exp(3*imag(polylog(2,exp(2*I*Pi/3)))/Pi) \\ _Charles R Greathouse IV_, Jul 14 2014
%Y A242711 Cf. A130834 (C_2), A242712 (C_4), A242713 (C_5), A242714 (C_6).
%K A242711 nonn,cons
%O A242711 1,2
%A A242711 _Jean-François Alcover_, May 21 2014

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