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I'm currently trying to solve this equation : x²[A+B.exp(x)]=1 for A and B real numbers, and x a complex (this comes from physics, so in my case, Re(x)>0)

I know that x.exp(x)=a has a solution using Lambert function : x=W(a)

I know that x².exp(x)=a may be recast to use the Lambert function, the solution being something like x=2W(sqrt(a)/2)

But what about my equation ? I tried a lot of things to recast the equation and use the Lambert function, but nothing, so I'm asking to you guys ...

Thanks

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# Generalized W Lambert function

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