All Questions
4 questions
13
votes
3
answers
544
views
Find asymptotics of $\sum\limits_{i=0}^{n/3} 2^i \binom{n-i-1}{\frac{2n}{3}-1}$
I have an expression
2^n / Sum[ 2^i Binomial[ n - i - 1, 2n/3 - 1], { i, 0, n/3}]
...
- 1,119
13
votes
2
answers
661
views
Asymptotics of $\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}}$
I am fairly sure that asymptotically $$\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}} \sim \frac{2}{\pi n}.$$
I tried
Limit[n*Sum[...
- 1,119
1
vote
1
answer
242
views
Discrepancy with Hurwitz Zeta function
I've come across an issue while using Wolfram Mathematica that I don't quite understand.
Consider the following symbolic computation:
...
- 27
0
votes
2
answers
491
views
Sum a certain hypergeometric-function-based expression pertaining to an integration problem
I would like to sum over the index $h$ from 3 to $\infty$, the expression
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- 2,385