Archive of posts with tag “combinatorics”
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A polynomial whose sum of coefficients is a factorial
The function $\left(1-z\right)^{n+1}\sum_{k=1}^\infty k^nz^k$ is a polynomial of degree $n$ w.r.t. $z$, and the sum of its coefficients is $n!$. This turns out to be properties of Eulerian numbers.
- Categories: math
- Tags: combinatorics, number sequence, from zhihu
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Solving linear homogeneous ODE with constant coefficients
By using power series, we can prove that the problem of solving linear homogeneous ODE with constant coefficients can be reduced to the problem of solving a polynomial with those coefficients. This article illustrates this point in detail, but it uses a very awful notation…
- Categories: math
- Tags: calculus, linear algebra, combinatorics, ode, long paper, from zhihu