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

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, 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, 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

Offset

1,2

References

Steven 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(5/Pi*Clausen2(Pi - Pi/5)), where Clausen2 is Clausen's Integral.

Example

1.967044901088071888351432414582828054693451...

Mathematica

Clausen2[x_] := Im[PolyLog[2, Exp[x*I]]]; c[m_] := Exp[m/Pi*Clausen2[Pi - Pi/m]]; RealDigits[c[5], 10, 100] // First

Prog

(PARI) exp(5*imag(polylog(2, exp(4*I*Pi/5)))/Pi) \\ Charles R Greathouse IV, Jul 15 2014

Crossrefs

Cf. A130834 (C_2), A242711 (C_3), A242712 (C_4), A242714 (C_6).

Sequence in context: A092513 A260315 A378485 * A155129 A254980 A318336

Adjacent sequences: A242710 A242711 A242712 * A242714 A242715 A242716

Keyword

nonn,cons

Author

Jean-François Alcover, May 21 2014

Status

approved