# Question:How to write procedures in MAPLE to deal with pseudo differential operators?

December 23 2013

1

I am trying to write procedures in MAPLE to deal with pseudo differential operators such as P=1+f_1D^{-1}+f_2D^{-2}+f_3D^{-3}+...,  where D=d/dx, f_i are functions of x. D^n for n<=0 work like usual differetial operators for n>=0. For example D^nD^m=D^{m+n}, D^n f=\sum_{i>=0}\binom{n}{i}(D^i f)D^{n-i}, where \binom{n}{i} are binomial coefficients given by n(n-1)...(n-i+1)/i! for n<= 0. I am wondering which package in MAPLE I could begin with, and how can I define D^{-1} and generally D^{-n}.

Thank you very much!

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