Very nice! Notice that if you write r=j−k,I as D−1, and play around with binomial coefficients a bit, we can rewrite this as:
D−k(fp)=∑∞r=0(−kr)(D−k−rf)(Drp)
which holds for k<0 as well, in which case it becomes the derivative product rule. This also matches the formal power series expansion of (x+y)−k, which one can motivate directly
Very nice! Notice that if you write r=j−k, I as D−1, and play around with binomial coefficients a bit, we can rewrite this as:
D−k(fp)=∑∞r=0(−kr)(D−k−rf)(Drp)
which holds for k<0 as well, in which case it becomes the derivative product rule. This also matches the formal power series expansion of (x+y)−k, which one can motivate directly
(By the way, how do you spoiler tag?)
Oh, very cool, thanks! Spoiler tag in markdown is: