

A242712


Decimal expansion of C_4, a constant related to sharp inequalities for the product of 4 polynomials, which was introduced by David Boyd.


3



1, 9, 4, 8, 4, 5, 4, 7, 8, 8, 9, 5, 8, 8, 3, 5, 6, 0, 6, 7, 0, 3, 1, 0, 2, 4, 6, 6, 8, 8, 6, 5, 7, 5, 5, 5, 8, 3, 0, 0, 7, 5, 8, 1, 7, 2, 0, 8, 8, 3, 4, 5, 8, 3, 8, 6, 1, 7, 8, 1, 6, 5, 3, 9, 0, 0, 8, 5, 9, 5, 9, 1, 3, 5, 0, 4, 1, 4, 2, 2, 0, 5, 9, 6, 4, 3, 4, 5, 9, 5, 5, 3, 3, 9, 4, 5, 7, 8, 1, 4
(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(4/Pi*Clausen2(Pi  Pi/4)), where Clausen2 is Clausen's Integral.


EXAMPLE

1.9484547889588356067031024668865755583...


MATHEMATICA

Clausen2[x_] := Im[PolyLog[2, Exp[x*I]]]; c[m_] := Exp[m/Pi*Clausen2[Pi  Pi/m]]; RealDigits[c[4], 10, 100] // First


PROG

(PARI) exp(4*imag(polylog(2, exp(3*I*Pi/4)))/Pi) \\ Charles R Greathouse IV, Jul 15 2014


CROSSREFS

Cf. A130834 (C_2), A242711 (C_3), A242713 (C_5), A242714 (C_6).
Sequence in context: A155821 A198218 A238183 * A010541 A103742 A092736
Adjacent sequences: A242709 A242710 A242711 * A242713 A242714 A242715


KEYWORD

nonn,cons


AUTHOR

JeanFrançois Alcover, May 21 2014


STATUS

approved



