User esg

24 votes

Binomial again, and again

answered Nov 18, 2016 at 19:21

21 votes

Accepted

Asymptotic expansion of $\sum\limits_{n=1}^{\infty} \frac{x^{2n+1}}{n!{\sqrt{n}} }$

answered Apr 2, 2017 at 13:15

14 votes

Accepted

Integral $\int_0^1 \int_0^1 \cdots \int_0^1\frac{x_{1}^2+x_{2}^2+\cdots+x_{n}^2}{x_{1}+x_{2}+\cdots+x_{n}}dx_{1}\, dx_{2}\cdots \, dx_{n}=?$

answered Dec 22, 2017 at 16:59

11 votes

What's the summation of formal series $\sum_{n\geq0}\binom{n\delta}{n}x^n$？

answered Nov 16, 2017 at 19:33

8 votes

Expected supremum of average?

answered Oct 20, 2017 at 17:53

8 votes

Accepted

The number of ways to merge a permutation with itself

answered Nov 11, 2020 at 19:35

7 votes

Accepted

A sum of two binomial random variables

answered Apr 28, 2020 at 20:03

7 votes

Alternative proofs sought after for a certain identity

answered Dec 19, 2020 at 14:10

7 votes

Comparing two power-series

answered Jul 27, 2021 at 16:01

7 votes

Accepted

Birthday problem with unequal probability: expected number of draws before the $m$-th collision?

answered Mar 4, 2017 at 19:24

7 votes

Eigenvalues of a matrix with entries involving combinatorics

answered Nov 29, 2016 at 17:36

6 votes

$\binom{x}{2}+\binom{x}{4}+\cdots+\binom{x}{2u}$ is a convex function on $[0,+\infty)$?

answered Sep 5, 2016 at 18:20

6 votes

A combinatorial identity

answered Aug 15, 2017 at 16:42

6 votes

Expected determinant of random symmetric matrix with different Gaussian distributions of the diagonal and non-diagonal elements

answered Dec 20, 2018 at 20:25

6 votes

Probability of getting exactly one head and $k$-wise independence

answered Nov 4, 2020 at 14:47

5 votes

Average distance of the mean of $n$ random complex numbers in a unit disc

answered Jun 22, 2021 at 16:51

5 votes

Accepted

Expected number of compositions needed to get constant function

answered Dec 1, 2021 at 19:12

5 votes

(Sharp) inequality for Beta function

answered Jan 1, 2019 at 19:45

5 votes

Accepted

Result attribution for eigenvalues of a matrix of Pascal-type

answered Aug 11, 2017 at 17:50

5 votes

Proof of a combinatorial equation

answered Aug 22, 2018 at 18:59

5 votes

Accepted

Under what conditions does the Mittag-Leffler function ${E_{\alpha ,1}}(z),(0 < \alpha < 1)$ has no real zero?

answered Apr 1, 2014 at 18:51

4 votes

$\prod_k(x\pm k)$ in binomial basis?

answered Feb 25, 2017 at 17:21

4 votes

Accepted

The probability density function of the number of coins to first fill one box of $N$

answered Sep 13, 2018 at 18:51

4 votes

Showing this formula counts these things

answered Nov 12, 2019 at 17:15

4 votes

Accepted

Moments of a combinatorial ensemble of random variables

answered Nov 15, 2019 at 20:36

4 votes

Quantifying the noninvertibility of a function

answered Nov 21, 2019 at 16:55

4 votes

Expected absolute value of the average of two points from the disc

answered Jun 22, 2021 at 16:55

3 votes

Accepted

Bounding the max-loaded bin using${m \choose k} \|A\|_k^k$

answered May 19, 2021 at 19:10

3 votes

Accepted

A polynomial identity related to Catalan numbers

answered Jan 25, 2023 at 17:37

3 votes

Grouping lists together in a proportional election: image of a Dirichlet distribution by the D'Hondt method of proportional allotment

answered May 22, 2023 at 19:47

Stack Exchange Network

56 Answers

Binomial again, and again

Asymptotic expansion of $\sum\limits_{n=1}^{\infty} \frac{x^{2n+1}}{n!{\sqrt{n}} }$

Integral $\int_0^1 \int_0^1 \cdots \int_0^1\frac{x_{1}^2+x_{2}^2+\cdots+x_{n}^2}{x_{1}+x_{2}+\cdots+x_{n}}dx_{1}\, dx_{2}\cdots \, dx_{n}=?$

What's the summation of formal series $\sum_{n\geq0}\binom{n\delta}{n}x^n$？

Expected supremum of average?

The number of ways to merge a permutation with itself

A sum of two binomial random variables

Alternative proofs sought after for a certain identity

Comparing two power-series

Birthday problem with unequal probability: expected number of draws before the $m$-th collision?

Eigenvalues of a matrix with entries involving combinatorics

$\binom{x}{2}+\binom{x}{4}+\cdots+\binom{x}{2u}$ is a convex function on $[0,+\infty)$?

A combinatorial identity

Expected determinant of random symmetric matrix with different Gaussian distributions of the diagonal and non-diagonal elements

Probability of getting exactly one head and $k$-wise independence

Average distance of the mean of $n$ random complex numbers in a unit disc

Expected number of compositions needed to get constant function

(Sharp) inequality for Beta function

Result attribution for eigenvalues of a matrix of Pascal-type

Proof of a combinatorial equation

Under what conditions does the Mittag-Leffler function ${E_{\alpha ,1}}(z),(0 < \alpha < 1)$ has no real zero?

$\prod_k(x\pm k)$ in binomial basis?

The probability density function of the number of coins to first fill one box of $N$

Showing this formula counts these things

Moments of a combinatorial ensemble of random variables

Quantifying the noninvertibility of a function

Expected absolute value of the average of two points from the disc

Bounding the max-loaded bin using${m \choose k} \|A\|_k^k$

A polynomial identity related to Catalan numbers

Grouping lists together in a proportional election: image of a Dirichlet distribution by the D'Hondt method of proportional allotment