OFFSET
1,2
COMMENTS
REFERENCES
R. Witula, D. Jama, D. Slota, E. Hetmaniok, Finite version of Carleman's and Knopp's inequalities, Zeszyty naukowe Politechniki Slaskiej (Gliwice, Poland) 92 (2010), 93-96.
LINKS
Steven R. Finch, Carleman's inequality, 2013. [Cached copy, with permission of the author]
Yu-Dong Wu, Zhi-Hua Zhang and Zhi-Gang Wang, The Best Constant for Carleman's Inequality of Finite Type, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, Vol. 24, No. 2, 2008
EXAMPLE
1.486353228963....
MATHEMATICA
RealDigits[c5/.FindRoot[{1+x2/2+x3/3+x4/4+x5/5==c5, x2/2+x3/3+x4/4+x5/5==c5*x2^2, x3/3+x4/4+x5/5==c5*x3^3/x2^2, x4/4+x5/5==c5*x4^4/x3^3, x5/5==c5*x5^5/x4^4}, {{c5, 3/2}, {x2, 1/2}, {x3, 1/2}, {x4, 1/2}, {x5, 1/2}}, WorkingPrecision->120], 10, 105][[1]] (* Vaclav Kotesovec, Oct 27 2014 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Roman Witula, Nov 16 2012
STATUS
approved