

A242714


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


3



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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


REFERENCES

S. 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: A247600 A281197 A199503 * A307715 A269547 A333345
Adjacent sequences: A242711 A242712 A242713 * A242715 A242716 A242717


KEYWORD

nonn,cons


AUTHOR

JeanFrançois Alcover, May 21 2014


STATUS

approved



