0
votes
0answers
31 views

Integral involving wavelet

Let $\hat{\psi}_m$ be a Fourier transform of Daubechies wavelet of order $m$ and $\chi_I$ is a characteristic function of interval $I$. How to bound from above the following integral $$ ...
4
votes
2answers
234 views

maybe this sum have approximation $\sum_{k=0}^{n}\binom{n}{k}^3\approx\frac{2}{\pi\sqrt{3}n}\cdot 8^n,n\to\infty$

prove or disprove this $$\sum_{k=0}^{n}\binom{n}{k}^3\approx\dfrac{2}{\pi\sqrt{3}n}\cdot 8^n,n\to\infty?$$ this problem is from when Find this limit ...
2
votes
0answers
96 views

approximating an integral/hypergeometric function

I am looking to approximate the following integral for small $z$: $\int_0^{\infty}dy \frac{1}{z} e^{-y/z} \frac{w e^{-y}}{s + w e^{-y}}$ . The integral can be solved in general to be a ...
2
votes
2answers
141 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
214 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
147 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 ...