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Jul
18
comment Compute $\sum_{b=2}^{\infty}{\left[\sum_{k=1}^{\infty}{\left(\frac{digitsum_b(k)}{k(k+1)}+\left(1+\frac1b\right)\frac{(-1)^k}{kb^k}\right)}\right]}$
Your conjecture is true. See here: mathworld.wolfram.com/DigitSum.html For techniques of calculating the sum, see this paper: cecm.sfu.ca/personal/pborwein/PAPERS/P56.pdf
Jul
18
comment Strong and weak laws of large numbers
See [this question][1] for a version of the strong law with some dependence assumptions. [1]: math.stackexchange.com/questions/1093047/… Generally you can easily prove the strong law by Chebyshev's inequality if you assume a fourth moment exists, so in doing this calculation, you can get away with both some dependence and even different distributions.
Jul
18
answered About 'Marcinkiewicz–Zygmund inequality'
Jul
18
comment Is $E[E[Y_tZ_t|Y_t]|\mathcal{F}_{t-1}] = E[Y_tZ_t|\mathcal{F}_{t-1}]$ where $\mathcal{F}_t$ is the natural filtration process
Double check your formatting, as you have a number of typographical errors.
Jul
18
awarded  sequences-and-series
Jul
17
revised What does this infinite product come out to?
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Jul
17
revised What does this infinite product come out to?
deleted 4 characters in body
Jul
17
answered What does this infinite product come out to?
Jul
17
comment Function defined by integrals convex?
Is $g$ allowed to equal 0 or is it strictly positive?
Jul
17
comment Name for a constrained Poisson-like bridge process
@DonkeyKong: I apologize if I've done a bad job explaining. The way to think about it is that it's a set of points $x_i$, say on $[0,1]$ after renormalization, where the nearest neighbor correlations are given by $f_i(t)$ which is the distribution of $x_{i+1}-x_i$.
Jul
17
answered generating function for $\frac{n!}{(2n)!}$
Jul
17
revised Summation of a series of Positive Prime numbers
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Jul
17
comment Nested… binomials coefficients?
Even if you mean $\binom{n}{\binom{n-1}{\binom{n-2}{\vdots}}}$, then $\binom{k}{k-1}=k$ so it would just be $n$.
Jul
16
revised Summation of a series of Positive Prime numbers
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Jul
16
comment Summation of a series of Positive Prime numbers
@HillyBilly: Sorry, I'm confused about what you're asking. Your question asks for the sum of primes in some set, and this answer shows asymptotic for calculating the sum of the first $n$ primes. I've added an edit.
Jul
16
comment Summation of a series of Positive Prime numbers
@HillyBilly: This is completely different. You're thinking of $\sum_{k=1}^N k^2=N(N+1)(2N+1)/6$.
Jul
16
comment Need to prove continuous periodic function of $\varphi (x) \equiv \psi(x)$
Is the $\equiv$ sign intentional or did you just mean $=$? If not please clarify.
Jul
16
answered Summation of a series of Positive Prime numbers
Jul
16
revised Name for a constrained Poisson-like bridge process
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Jul
16
asked Name for a constrained Poisson-like bridge process