

A242713


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


3



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
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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(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: A195365 A092513 A260315 * A155129 A254980 A318336
Adjacent sequences: A242710 A242711 A242712 * A242714 A242715 A242716


KEYWORD

nonn,cons


AUTHOR

JeanFrançois Alcover, May 21 2014


STATUS

approved



