A244238 - OEIS

A244238

Decimal expansion of K = exp(8*G/(3*Pi)), a Kneser-Mahler constant related to an asymptotic inequality involving Bombieri's supremum norm, where G is Catalan's constant. K can be evaluated as Mahler's generalized height measure of the bivariate polynomial (1+x+x^2+y)^2.

%I #10 Sep 08 2022 08:46:08

%S 2,1,7,6,0,1,6,1,3,5,2,9,2,3,7,0,4,2,6,2,3,5,1,6,0,7,6,5,7,3,2,3,2,7,

%T 3,7,1,6,7,7,3,2,6,6,1,3,7,1,5,4,2,2,2,5,5,1,6,3,7,8,9,8,2,3,2,2,0,2,

%U 2,9,6,8,2,8,7,0,1,8,0,2,6,0,0,7,6,6,8,5,5,0,9,2,8,5,3,4,2,5,3,1,1,9

%N Decimal expansion of K = exp(8*G/(3*Pi)), a Kneser-Mahler constant related to an asymptotic inequality involving Bombieri's supremum norm, where G is Catalan's constant. K can be evaluated as Mahler's generalized height measure of the bivariate polynomial (1+x+x^2+y)^2.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.10 Kneser-Mahler polynomial constants, p. 234.

%H G. C. Greubel, <a href="/A244238/b244238.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/BombieriNorm.html">Bombieri Norm</a>

%e 2.17601613529237042623516...

%t RealDigits[Exp[8*Catalan/(3*Pi)], 10, 102] // First

%o (PARI) default(realprecision, 100); exp(8*Catalan/(3*Pi)) \\ _G. C. Greubel_, Aug 25 2018

%o (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Exp(8*Catalan(R)/(3*Pi(R))); // _G. C. Greubel_, Aug 25 2018

%Y Cf. A006752, A242908, A242909, A242910.

%K nonn,cons,easy

%O 1,1

%A _Jean-François Alcover_, Jun 23 2014