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A242710 Decimal expansion of "beta", a Kneser-Mahler polynomial constant (a constant related to the asymptotic evaluation of the supremum norm of polynomials). 3
1, 3, 8, 1, 3, 5, 6, 4, 4, 4, 5, 1, 8, 4, 9, 7, 7, 9, 3, 3, 7, 1, 4, 6, 6, 9, 5, 6, 8, 5, 0, 6, 2, 4, 1, 2, 6, 2, 8, 9, 6, 3, 7, 2, 6, 2, 2, 3, 9, 0, 7, 0, 5, 6, 0, 1, 9, 8, 7, 6, 4, 8, 4, 5, 3, 0, 0, 5, 5, 4, 9, 6, 3, 6, 3, 6, 6, 3, 6, 2, 4, 5, 4, 0, 8, 6, 3, 9, 7, 6, 7, 9, 5, 4, 4, 2, 8, 1, 1, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 3.10 Kneser-Mahler polynomial constants p. 232 and Section 5.23 Monomer-dimer constants p. 408.

LINKS

Table of n, a(n) for n=1..100.

Kurt Mahler, A remark on a paper of mine on polynomials.,[In this paper, j is log(beta)]

Eric Weisstein's MathWorld, Gieseking's Constant

FORMULA

beta = exp(G/Pi) = exp((PolyGamma(1, 4/3) - PolyGamma(1, 2/3) + 9)/(4*sqrt(3)*Pi)), where G is Gieseking's constant (cf. A143298) and PolyGamma(1,z) the first derivative of the digamma function psi(z).

Also equals exp(-Im(Li_2( 1/2 - (i*sqrt(3))/2))/Pi), where Li_2 is the dilogarithm function.

EXAMPLE

1.38135644451849779337146695685...

MATHEMATICA

Exp[(PolyGamma[1, 4/3] - PolyGamma[1, 2/3] + 9)/(4*Sqrt[3]*Pi)] // RealDigits[#, 10, 100]& // First

CROSSREFS

Cf. A130834, A143298, A229728.

Sequence in context: A140272 A210962 A021728 * A084185 A073227 A016550

Adjacent sequences:  A242707 A242708 A242709 * A242711 A242712 A242713

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, May 21 2014

STATUS

approved

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Last modified December 7 11:32 EST 2016. Contains 278874 sequences.