Landau-Kolmogorov Constants

Author

Eric W. Weisstein
October 17, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/Landau-KolmogorovConstants.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Landau-KolmogorovConstants.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Kolmogorov

a[n_]:=(4/π)Sum[(((((((-1))^j)/(2j+1))))^(n+1)),{j,0,∞}]

a[n]

c[n_,k_]:=a[n-k]((a[n])^(k/n-1))

((c[3,1])^3)//FullSimplify

c[3,2]

((c[4,1])^4)//FullSimplify

((c[4,2])^2)//FullSimplify

((c[4,3])^4)//FullSimplify

((c[5,1])^5)//FullSimplify

((c[5,2])^5)

Hardy

Integrate[(1/(((x^(2n))-y (x^2)+1)(Sqrt[y]))),{x,0,c},{y,0,∞}]

Integrate[(1/(((x^(2n))-y (x^2)+1)(Sqrt[y]))),{x,0,c},{y,0,∞},Assumptions->c>0]