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