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Bumped by Community user
Bumped by Community user
Bumped by Community user
edited tags, added name to function
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YCor
YCor
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I would like to evaluate the asymptotic value of the following sum:

$$\frac{1}{2^N}\sum_{n=0}^{N} \binom{N}{n} \log_{2} \binom{N}{n}$$$$f(N)=\frac{1}{2^N}\sum_{n=0}^{N} \binom{N}{n} \log_{2} \binom{N}{n}$$

This is related to the computation of the Shannon entropy. Any help would be greatly appreciated!

I would like to evaluate the asymptotic value of the following sum:

$$\frac{1}{2^N}\sum_{n=0}^{N} \binom{N}{n} \log_{2} \binom{N}{n}$$

This is related to the computation of the Shannon entropy. Any help would be greatly appreciated!

I would like to evaluate the asymptotic value of the following sum:

$$f(N)=\frac{1}{2^N}\sum_{n=0}^{N} \binom{N}{n} \log_{2} \binom{N}{n}$$

This is related to the computation of the Shannon entropy. Any help would be greatly appreciated!

Bumped by Community user
Added tag, improved LaTeX'ing. I had never seen binomial coefficients as matrices!
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edit approved Apr 12, 2019 at 7:30
Rodrigo de Azevedo
edit approved Apr 12, 2019 at 7:30
Rodrigo de Azevedo
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I would like to evaluate the asymptotic value of the following sum:

$\frac{1}{2^N}\sum_{n=0}^{N} \begin{pmatrix}N\\ n \end{pmatrix} \text{log}_{2} \begin{pmatrix}N\\ n \end{pmatrix}$. This$$\frac{1}{2^N}\sum_{n=0}^{N} \binom{N}{n} \log_{2} \binom{N}{n}$$

This is related to the computation of the Shannon entropy. Any help would be greatly appreciated!

I would like to evaluate the asymptotic value of following sum:

$\frac{1}{2^N}\sum_{n=0}^{N} \begin{pmatrix}N\\ n \end{pmatrix} \text{log}_{2} \begin{pmatrix}N\\ n \end{pmatrix}$. This is related to the computation of the Shannon entropy. Any help would be greatly appreciated!

I would like to evaluate the asymptotic value of the following sum:

$$\frac{1}{2^N}\sum_{n=0}^{N} \binom{N}{n} \log_{2} \binom{N}{n}$$

This is related to the computation of the Shannon entropy. Any help would be greatly appreciated!

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Ryan
Ryan
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Asymptotic value of the Shannon entropy

I would like to evaluate the asymptotic value of following sum:

$\frac{1}{2^N}\sum_{n=0}^{N} \begin{pmatrix}N\\ n \end{pmatrix} \text{log}_{2} \begin{pmatrix}N\\ n \end{pmatrix}$. This is related to the computation of the Shannon entropy. Any help would be greatly appreciated!