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A242713 Decimal expansion of C_5, a constant related to sharp inequalities for the product of 5 polynomials, which was introduced by David Boyd.

%I A242713 #13 Feb 16 2025 08:33:22
%S A242713 1,9,6,7,0,4,4,9,0,1,0,8,8,0,7,1,8,8,8,3,5,1,4,3,2,4,1,4,5,8,2,8,2,8,
%T A242713 0,5,4,6,9,3,4,5,1,3,8,7,7,1,2,7,5,8,1,5,6,6,4,2,0,8,4,3,8,7,0,3,6,4,
%U A242713 0,2,9,2,7,3,0,3,9,5,2,6,8,1,2,6,3,1,4,1,8,3,9,4,3,5,2,1,2,1,6,7
%N A242713 Decimal expansion of C_5, a constant related to sharp inequalities for the product of 5 polynomials, which was introduced by David Boyd.
%D A242713 Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 3.10 p. 233.
%H A242713 David W. Boyd, <a href="https://citeseerx.ist.psu.edu/pdf/522373ad9d2ff1a77a4054e6c28d8da3df682e5d">Sharp inequalities for the product of polynomials</a>
%H A242713 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/ClausensIntegral.html">Clausen's Integral</a>
%F A242713 exp(5/Pi*Clausen2(Pi - Pi/5)), where Clausen2 is Clausen's Integral.
%e A242713 1.967044901088071888351432414582828054693451...
%t A242713 Clausen2[x_] := Im[PolyLog[2, Exp[x*I]]]; c[m_] := Exp[m/Pi*Clausen2[Pi - Pi/m]]; RealDigits[c[5], 10, 100] // First
%o A242713 (PARI) exp(5*imag(polylog(2, exp(4*I*Pi/5)))/Pi) \\ _Charles R Greathouse IV_, Jul 15 2014
%Y A242713 Cf. A130834 (C_2), A242711 (C_3), A242712 (C_4), A242714 (C_6).
%K A242713 nonn,cons
%O A242713 1,2
%A A242713 _Jean-François Alcover_, May 21 2014