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seen Apr 11 at 18:17

Oct
21
awarded  Commentator
Oct
21
comment Condition so that coefficients nilpotent implies power series nilpotent for non-noetherian ring $R$ with char$(R) = 0$
Sorry, I should've specified that I was looking for a necessary and sufficient condition - I'm looking to describe "what the nilpotent elements of R[[X]] look like", so to speak. Theorem 2 gives a sufficient but not necessary condition, and I believe Corollary 1 does too (where the sufficient but not necessary part is that $A_f$ has to be finitely generated).
Oct
21
revised Condition so that coefficients nilpotent implies power series nilpotent for non-noetherian ring $R$ with char$(R) = 0$
added 94 characters in body
Oct
20
comment Condition so that coefficients nilpotent implies power series nilpotent for non-noetherian ring $R$ with char$(R) = 0$
@MartinBrandenburg I had already read the first one, which confirmed the things I mentioned in my post but didn't answer the question. I've just read the second one, but again it only confirms my post (unless I misread something).
Oct
20
asked Condition so that coefficients nilpotent implies power series nilpotent for non-noetherian ring $R$ with char$(R) = 0$
Oct
18
accepted Nilradical of $\mathbb{R}[X,Y]/(X^nY^m)$
Oct
10
asked Nilradical of $\mathbb{R}[X,Y]/(X^nY^m)$
May
25
accepted Summation with factorial terms (involving Laguerre polynomials)
May
25
comment Summation with factorial terms (involving Laguerre polynomials)
Thanks! I used the same reasoning with the poles of the gamma, but turned it into a summation rather than changing the order of integration.
May
25
comment Summation with factorial terms (involving Laguerre polynomials)
Perhaps I should've mentioned this, but Laguerre polynomials aren't actually part of my course and this exercise is where they were first introduced, so I would not be allowed to use this property without proving it first. Would it be wise to prove this property or to continue looking for a more direct solution?
May
25
comment Summation with factorial terms (involving Laguerre polynomials)
The definition as given by the exercise would be $$P_n(x) = \frac{(-1)^nn!}{2\pi i} \oint_\Sigma \frac{\Gamma(t-n)}{\Gamma(t+1)^2}x^tdt.$$ where $\Sigma$ is a closed curve that goes around the points $0, 1, \dots, n$ counterclockwise once.
May
25
asked Summation with factorial terms (involving Laguerre polynomials)
May
25
accepted Generating Laguerre polynomials using gamma functions
May
25
revised Generating Laguerre polynomials using gamma functions
deleted 101 characters in body
May
24
comment Generating Laguerre polynomials using gamma functions
Legendre polynomials have this property because, if $n$ is even/odd, then all powers of $x$ are even/odd. Laguerre polynomials of degree $n$ have terms with every power of $x$ (being $0, 1, \dots, n$) so this property doesn't hold, unfortunately.
May
24
asked Generating Laguerre polynomials using gamma functions
May
3
accepted Rouché's Theorem on $z^{10} + 10z + 9$
May
3
asked Rouché's Theorem on $z^{10} + 10z + 9$
Apr
16
accepted Stochastic variable equals indicator function?
Apr
15
comment Stochastic variable equals indicator function?
An indicator function always made me think of uniform distribution, but the way you put it, it would be a Bernoulli distribution with $p = \frac{1}{2} + \frac{1}{n}$, which would converge to $X$ because that s.v. has a Bernoulli distribution with $p = 1/2$?