A178422 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.

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, 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, 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

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..105.

Example

2.752343784475978738378526211574397572882090586248...

Prog

(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

Crossrefs

Sequence in context: A201319 A110945 A197571 * A296564 A266262 A105387

Adjacent sequences: A178419 A178420 A178421 * A178423 A178424 A178425

Keyword

cons,nonn

Author

Artur Jasinski, May 27 2010

Status

approved