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Results tagged with sequences-and-series
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user 136807
for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
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About a multiple integral [closed]
In my current research, I'm confronted with the justification of some facts, and I don't know how to proceed in proving them, so I need to know if there exist some theorems (precisely three theorems) …
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answer
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Upper bound over $[0,1] $ for strange family of polynomials
Let $n$ integer $\geq 2,$ $x$ real, and $$P_n(x)=\displaystyle \sum_{k=0}^{n-1} C_{n+k}^n (-x)^k \alpha_{n,k}$$ and where $\forall k$ such that $0 \leq k \leq n-1 $ $$ \alpha_{n,k}= \displaystyle …
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Alternative approaches to Zudilin's proof of Apéry's theorem
The article
Wadim Zudilin, Apéry's theorem. Thirty years after, Int. J. Math. Comput. Sci. 4 (2009), no. 1 pp 9–19. (arXiv:math/0202159, with the title An elementary proof of Apéry's theorem)
in …
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Recurrence involving families of orthogonal polynomials
Let $ \forall n \in N, n\geq 1$ $$ R_n(x)=(-1)^n n! \displaystyle \frac{(x-1)...(x-n)}{(x(x+1)..(x+n))^2}$$ thus by decomposition in simple element it's easy to see that
$$ (1): \quad R_n(x)= \displ …
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