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I have the following recurrence relation: x(1)=1$, x(2)=t and x(n+2)=(t*x(n-1)-d^(n-3)*x(n))/d^n

where t and d are variables and n is any natural number.

When we assign values to n we obtain rational functions in terms of t and d.

I would like to use a software that shows me the first 50 rational functions, i.e. x(3), x(4),..., x(50).

The problem is I do not know any software that can do this for me. Do you know one?

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Hope I understand your request right. What you are searching for is a program which computes recursively defined functions symbolic.

A lot of professional mathemtical software exists which can handle your task, like

  • Matlab
  • Maple
  • Mathematica

If you prefer free software as I do use

  • Python with the SymPy package
  • Octave
  • Sage

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