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seen Dec 5 '13 at 8:19

Come here to write articles about mathematics, or discussion is welcome as well.

Voofie/Mathematics


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19
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24
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Sep
16
answered differential-difference three-term recursion
Aug
18
accepted Why relativization can't solve NP !=P?
Aug
15
asked Why relativization can't solve NP !=P?
Aug
6
comment Recursions which define polynomials
From another comment: "Can you give me some hints on how to generate (say, nontrivially) polynomials from your final formula, having a rational function a(t) ? Thanks! " He asked for method to generate polynomial from Max Alekseyev's formula. So I think providing a method is good enough.
Aug
6
comment Recursions which define polynomials
"I could not find any other example of a polynomial sequence generated in this way. I simply look for another such sequence of polynomials, so if you've ever seen something similar, please let me know. One more example would be a good answer to my question.", from author's comment. He just asked for 1 more example. And there is no mention of surprise?
Aug
6
revised Recursions which define polynomials
added 299 characters in body; added 80 characters in body
Aug
6
answered Recursions which define polynomials
Aug
2
revised Solving partial difference equation
edited tags
Aug
1
comment Solving partial difference equation
Furthermore, for the Eulerian numbers, the order of difference equation for both the variables k and n are 1. But for the equation I asked, it is first order in n, but 2nd order in k. So I think they differ quite a lot.
Jul
27
comment Explicit formula for Euler zigzag numbers(Up/down numbers)
Wadim, you are right. It is really an explicit formula. I didn't notice it since I don't know Euler polynomials has explicit expansion. However, the formula you provided has an absolute sign. I think it will make all the manipulation and computation inconvenient?
Jul
27
comment Solving partial difference equation
You are right, Zudilin. Are you interested in finding a close form solution? Btw, the zigzags are just the tangent and secant number. Therefore that's not really mine.
Jul
27
comment Solving partial difference equation
Thank you for your answer. I read the page you mentioned in wikipedia. There is indeed closed form to Eulerian numbers: $A(n,m)=\sum_{k=0}^{m}(-1)^k \binom{n+1}{k} (m+1-k)^n.$ I don't know if I read it wrongly or not. Thanks!