Question: How do I evaluate the inverse of the Poisson Loss Function?

I'm hoping somebody can help with this problem.

The Poisson Loss Function is defined by the series:

L := sum((n-s)*lambda^n*exp(-lambda)/factorial(n), n = s .. infinity)

Where lambda is the mean value that is prescribed and s is the variable in question.

Now, if the value of L is given, can anyone tell me how to solve for  s?

Poisson Distribution Loss Function Tables are available and give values for s for a given lambda, so I's like to see if Maple can handle this.


Thanks for reading!

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