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Results tagged with co.combinatorics
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user 60457
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
4
votes
2
answers
497
views
Ordinary or Rational Generating Function for Associated Stirling Numbers $b(n,k)$
I am trying to identify or find the ordinary or rational generating function (not the exponential generating function) for the Associated Stirling numbers of the Second kind, denoted $$b(1;n,k)=b(n,k) …
2
votes
0
answers
154
views
Unrestricting The Parameters of a Functional Equation
Good evening. I am looking into methods of generalization of Bernoulli polynomials. First, define
$$\Phi_{N,k}(x)=\frac{1}{N}\sum_{j=0}^{N-1}\omega_N^{-jk}\exp\left(\omega_N^jx\right)$$
where $\o …
2
votes
1
answer
213
views
Coefficients for Powers of the Mittag-Leffler Function
Considering the one parameter Mittag-Leffler function,
$$E_{\alpha}(z)=\sum_{k=0}^\infty\frac{z^{k}}{\Gamma(\alpha k+1)}, \Re(\alpha)>0$$
Considering then the generating function for $E_\alpha(z^\a …