Question

Can I write (j+1)(j+2)(j+3)......(j+n) = (j+n)!
Please

Answer 1

Only if j=0 or j=1

Answer 2

P.S. (j+1)(j+2)(j+3)......(j+n) = (j+n)! / j!

Answer 3

Thank you

Answer 4

no problem

Answer 5

I have problem with express the stuff: S, D are linear transformations on P
P(t) = \(\sum_{j=0}^{n-1} \xi_j t^j\)
SP(t) = \(\sum_{j=0}^{n-1} \dfrac{\xi_j}{j+1} t^{j+1}\)
DP(t) = \(\sum_{j=0}^{n-1} j\xi_j t^{j-1}\)
calculate \(D^nS^n\) and \(S^nD^n\)

Answer 6

If using D, S as differentiation and integration, it's quite easy to calculate.
In this case, I have to use those notations to calculate :(