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A178422 Decimal expansion of constant k such that function (x^2+1)^(1/x)+(x^2-1)^(1/x) is maximum for x=k. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is solution of 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

Constant k=2.752343784...

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

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Last modified August 8 14:04 EDT 2020. Contains 336298 sequences. (Running on oeis4.)