# Tagged Questions

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### Has anyone seen this series?

I come across the following infinite series. $$\sum_{n=1}^{\infty} \frac{t^n}{n!\: n^{a}}, \quad\text{for t>0 and a>0}.$$ In particular, I am interested in the case where $a=1/4$. ...
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### Passing to the limit in a PDE (subsequence problems)

For $w \in L^2(0,T;H^1)$, consider the PDE $$\int u'(t)v(t) + \int g(w(t))\nabla u(t) \nabla v(t) = \int f(t) v(t)\quad \forall v \in L^2(0,T;H^1)$$ where $u \in H^1(0,T;L^2)\cap L^2(0,T;H^1)$, and $f$...
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### series representation of bivariate functions

Given a bivariate function $f(x, y)$ with $x \in [-a,a]$ and $y \in [-b, b]$, what is the necessary and sufficient condition under which we can write $f(x, y) = \sum g_k(x)h_k(y)$ for all $(x,y)$ in ...
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### Asymptotic behaviour of sequence

I am interested in the sequence $$a(n)=\sum_{k=0}^n {p(n-k) \choose k}$$ where $p(n)$ is a polynomial equation. When $p(n)=n$ this reduces to the Fibonacci sequence, but what about when $p(n)$ is ...
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### Series of the inverse quadratic trinomial

Maybe it's a very simple question, but I have a problem with the following series $$\sum\limits_{n=1}^{\infty}\frac{1}{n^2+pn+q},$$ where $p, q \in \mathbb{R}$. I know about five ways how to calculate ...
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### norm of the matrix series

The goal is to obtain an upper bound for the norm of the vector $$\left\|\sum\limits_{k=0}^{\infty}(I−A)^kAw_k\right\|$$ for any symmetric matrix $A\in{\mathbb R}^{n×n}$ which $0\preceq A\preceq I$ ...
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### Can an infinite number of mathematicians guess the number in a box with only one error?

In this question the following observation was made: Consider a sequence of boxes numbered 0, 1, ... each containing one real number. The real number cannot be seen unless the box is opened. Define ...
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### Extending a Certain Result from Locally Convex Topological Vector Spaces to General Topological Vector Spaces

In this Math Stack Exchange post, I proved the following result. Theorem: Let $X$ be a locally convex topological vector space. Let $x \in X$ and suppose that $(x_{n})_{n \in \mathbb{N}}$ is ...
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### Convergence of $\sum_{n=1}^\infty \frac{\psi^{(1)}(1-n/\pi)}{n^3}$

Related to an open problem about another series. Set $$A= \sum_{n=1}^\infty \frac{\psi^{(1)}(1-n/\pi)}{n^3}$$ where $\psi^{(n)}(k)$ is the polygamma function. Does $A$ converge? The related ...