login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 27 04:47 EST 2014. Contains 250155 sequences.