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Product of three or more independent sub-Gaussian varibles

As indicated in the comment, the boundedness can be used to prove that the product is sub-Gaussian. Suppose $X_{1}, \ldots, X_{n}$ are bounded such that for $i \in [n]$ there exists a constant such ...
doshi's user avatar
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3 votes
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Ask for a generating function or an explicit expression of a triangle of positive integers

The generating function: $${\cal C}(x,y) = \sum_{n,k\geq 0} C_{n,k} x^n y^{2k}$$ has the following explicit form: $${\cal C}(x,y) = \frac{\arctan(y)}{y(1-x(1+y^2))}.$$ For "one more problem",...
Max Alekseyev's user avatar
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Identities for the generating functions of a sort of convolution powers of the Narayana numbers

First off, it should be added that $C_0(t)=1$, which does not follow from the given formula. Let's show that $$h_{2k+1}(x,t) = L_{2k}(1-(1+t)x,-tx^2)tx + L_{2k+2}(1-(1+t)x,-tx^2).$$ First notice that $...
Max Alekseyev's user avatar

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