On Tue, Sep 20, 2016 at 12:35:18PM +0000, Basile B. via Digitalmars-d-learn
wrote:
[...]
> The problem is here:
> https://github.com/BBasile/iz/blob/master/import/iz/math.d#L849
> - f(x,c) = 1.0 - pow(1.0 - pow(x, 2.0/c), c * 0.5);
> - c(f0.5)) = ?
>
> Which means that I ask you if you can isolate c for
>
> y = 1.0 - pow(1.0 - pow(0.5, 2.0/c), c * 0.5);
>
> y is always f(0.5,c)

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I couldn't manage to solve it. Nested exponentials are very nasty to
invert. :-( At first, I thought it might be solvable in terms of the
Lambert W function (aka ProductLog) but I couldn't manage to get the
equation into the right form. Then I checked on Wolfram Alpha and it
says "no result found in terms of standard mathematical functions".
That probably means the inverse cannot be expressed in terms of
elementary functions. Probably the only thing you can do is to use some
kind of numerical approximation, like some form of Newton's method or
some such, to find the value of c.
T
--
Questions are the beginning of intelligence, but the fear of God is the
beginning of wisdom.