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LambertWSolver

Description

Summary

K (alpha x + beta) b^(gamma x + delta) = c, a linear function times an exponential of
another, solved by the Lambert W function. https://github.com/asc-community/AngouriMath/issues/2182

Remarks

Written e^((gamma x + delta) ln b), the exponent is u = g x + d, and with
s = beta g / alpha - d the equation is (u + s) e^(u + s) = A,
A = c g e^s / (K alpha), so u + s = W(A) and x = W(A) / g - beta / alpha.
Over the complex numbers every branch is a root, W_n for a whole n, as a periodic
equation's roots are written. Over the reals two branches can be: W_0 where
A >= -1/e and W_(-1) where -1/e <= A < 0, and none where
A < -1/e, since w e^w >= -1/e for every real w.

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LambertWSolver

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