On Tuesday, 20 September 2016 at 16:22:19 UTC, H. S. Teoh wrote:
On Tue, Sep 20, 2016 at 12:35:18PM +0000, Basile B. via Digitalmars-d-learn wrote: [...]
The problem is here:
- 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)

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.


Thanks for trying, you're not the first to tell me about the Newton's method...

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