%I #13 Jan 15 2021 13:27:57

%S 2,7,5,2,3,4,3,7,8,4,4,7,5,9,7,8,7,3,8,3,7,8,5,2,6,2,1,1,5,7,4,3,9,7,

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

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

%N Decimal expansion of the constant c such that the function (x^2+1)^(1/x) + (x^2-1)^(1/x) is maximized at x=c.

%C This is the solution of the transcendental equation: (-1 + x^2)^(1/x) (2/(-1 + x^2) - log(-1 + x^2)/x^2) + (1 + x^2)^(1/x) (2/(1 + x^2) - log(1 + x^2)/x^2) = 0.

%e 2.752343784475978738378526211574397572882090586248...

%o (PARI) solve(x=2, 3, (-1 + x^2)^(1/x) * (2/(-1 + x^2) - log( -1 + x^2)/x^2) + (1 + x^2)^(1/x) * (2/(1 + x^2) - log(1 + x^2)/x^2)) \\ _Michel Marcus_, Sep 09 2013

%K cons,nonn

%O 1,1

%A _Artur Jasinski_, May 27 2010