Tagged Questions
2
votes
2answers
82 views
Sequence of polynomials converging to zero function
Find a sequence of polynomials $(f_n)$ such that $f_n \rightarrow 0$ point wise on $[0,1]$ and $\int_0^1 f_n(x) \rightarrow 3$. Calculate $\int_0^1 \sup_n |f_n(x)| dx$ for this sequence of ...
5
votes
1answer
178 views
prove equality with integral and series
I am stuck on one question with integral. Help me please to show that with $n=1$ the following is true
$$
...
1
vote
0answers
132 views
integral with Bessel function
Let $n$ be half an odd integer, say $n=k+1/2, k \in Z$. Let $q\geq 1$. I would like to calculate (or approximate) the following integral
$$
\int_0^{\infty}\left(\sqrt{\frac{\pi}{2}}\cdot 1\cdot 3\cdot ...
