Differential operator D as an algebraic quantity???

[vedaprabhu]

Hello!

while solving a linear differential equation of general form we often use the
differential operator"D" as an algebraic quantity.

Say in expansion of f(d)=[1/(D-1)]q(x) we write f(d)=(D-1)^-1 and expand using binomial expansion.But binomial expansion is valid only for |D|<1 right?!...

I wonder how to interprete an "operator D" to be less than 1 or not...could somebody explain?:|

 

[cherrytart]

A differo-integral or differintegral allows for derivatives of arbitrary order, used in fractional calculus. Differentiation to negative power is just an integral (hence the dual nature of the name).
I have no idea how this applies to operator theory but maybe the terms will help you search.