Marko Riedel
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 41 How many connected graphs over V vertices and E edges? 19 Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$ 17 Compute $\sum_{k=1}^{\infty}e^{-\pi k^2}\left(\pi k^2-\frac{1}{4}\right)$ 16 Sum the series $\sum_{n = 1}^{\infty}\{\coth (n\pi x) + x^{2}\coth(n\pi/x)\}/n^{3}$ 16 Proof of $\frac{1}{e^{\pi}+1}+\frac{3}{e^{3\pi}+1}+\frac{5}{e^{5\pi}+1}+\ldots=\frac{1}{24}$

### Reputation (24,256)

 +10 Combinatorial identity's algebraic proof without induction. +10 The number of $n$-tuples of nonnegative integers $(x_1,\ldots,x_n)$ satisfying the equation $x_1+\cdots+x_n = r$ +18 Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k}$ +5 Zeta function values in terms of Bernoulli numbers.

### Questions (14)

 8 average order of $\sum\limits_{\substack{1\le k\le n \\ (k,n)=1}} \frac{1}{k}$ 8 the constant in the asymptotics of $\sum_{1\le k \le n} \frac{\varphi(k)}{k^2}$ 7 unorthodox solution of a special case of the master theorem 7 stirling numbers and harmonic number identities 7 asymptotics of the expected number of edges of a random acyclic digraph with indegree and outdegree at most one

### Tags (212)

 720 combinatorics × 488 143 graph-theory × 54 457 sequences-and-series × 126 142 calculus × 39 284 binomial-coefficients × 197 137 complex-analysis × 46 267 summation × 158 131 number-theory × 62 171 generating-functions × 84 108 integration × 41

### Account (1)

 Mathematics 24,256 rep 22174