A242712 Decimal expansion of C_4, a constant related to sharp inequalities for the product of 4 polynomials, which was introduced by David Boyd.

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

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

Jean-François Alcover, May 21 2014

Status

approved