Re: x^x = 1/4

Gib Bogle <bogle@xxxxxxxxxxxxxxxxxxxxxxxx> wrote:
> john wrote:
>> Easily done. here is a list, also from MathCad, for x^x = a,
>> 0.2 <= a <= 0.9

>> 0.2 -0.0111293901917468-1.01739249615655i
>> 0.3 0.107262163062439+0.821526901788799i
>> 0.4 0.193822522073504+0.656549581040713i
>> 0.5 0.262892828009026+0.499669435669579i
>> 0.6 0.320971270023043+0.327577921754899i
>> 0.7 0.462337531535098
>> 0.8 0.739533650012175
>> 0.9 0.888135328827093

>> john

> The behaviour after a = 0.3 is smooth, but the jump from 0.2 to 0.3 is
> pretty dramatic, ...

If you're speaking of the change of sign of the imaginary, that's
meaningless. Any solution to x^x equals a real number has another
solution with the opposite sign on the imaginary, i.e. the complex
conjugate.
--
Keith F. Lynch - http://keithlynch.net/
Please see http://keithlynch.net/email.html before emailing me.
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