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Let $D=x\frac{d}{dx}$ and $A_i\in\mathbb{R}[[x]]$ for $i=1,...,n$. Let $B_i\in\mathbb{R}[[x]]$ for $i=1,...,n$ such that $$(D-A_n)...(D-A_1)=D^n+\sum_{i=1}^nB_iD^{n-i}.$$

Is there a well-known formula for $B_i$?

Also, suggestions for the resources for the factorization of linear differential operators are appreciated.

Platonicsolids
  • 390
  • Does the notation $A_i \in \mathbb{R}[[x]]$ denote that $A_i$ are polynomials in $x$ with real coefficients, or something else (e.g., formal power series)? – akkapi Mar 29 '22 at 12:38
  • Actually answer does not change in any case. But it is formal power series over field real numbers. – Platonicsolids Mar 30 '22 at 01:52

0 Answers0