.GNU_ScientificLibrary.Blocks.specfunc.NumericalInversions.SolveExpTranscend

Information

This block solves an exponential-transendental equation of the form:

x = a + b ecx

where b and c must be nonzero. The solution is found via the Lambert W functions:

x = a - W(-bc eac) / c 

where W(y) is a solution of: W(y) eW(y) = y .

If the argument (y = -bc eac) of the W function is real and between -1/e and 0, then there are two real W values: W0 (> -1) and W-1 (< -1).
If the argument is real and >=0, then there is one real value: W0.

The boolean outputs bx[1] and bx[2] denote whether real solutions for x exist. If their values are "true", then the corresponding x values contain the solutions: x[1] from W0 and x[2] from W-1.

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