non linear fit of multiple data sets with recursive function

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Hello every one
I am in trouble with a fit because I am working with a recursive function and I am not able to write a code to correctly fit my data. Morover, I have to fit several data set at the same time.
The fitting function is: , where . In this expression, . In essence, the functions τ and are interconnected and I have no idea in which way write these two in my fitting code.
The perameters I want to know are: while the quantities I know are .
Do you have any idea on the way to write this code?

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