# Tagged Questions

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 $$... 2answers 270 views ### maybe this sum have approximation \sum_{k=0}^{n}\binom{n}{k}^3\approx\frac{2}{\pi\sqrt{3}n}\cdot 8^n,n\to\infty prove or disprove this$$\sum_{k=0}^{n}\binom{n}{k}^3\approx\dfrac{2}{\pi\sqrt{3}n}\cdot 8^n,n\to\infty?$$this problem is from when Find this limit ... 0answers 103 views ### approximating an integral/hypergeometric function I am looking to approximate the following integral for small z: \int_0^{\infty}dy \frac{1}{z} e^{-y/z} \frac{w e^{-y}}{s + w e^{-y}} . The integral can be solved in general to be a ... 2answers 143 views ### Sequence of polynomials converging to zero function Find a sequence of polynomials (f_n) such that f_n \rightarrow 0 point wise on [0,1] and \int_0^1 f_n(x) \rightarrow 3. Calculate \int_0^1 \sup_n |f_n(x)| dx for this sequence of ... 1answer 215 views ### prove equality with integral and series I am stuck on one question with integral. Help me please to show that with n=1 the following is true$$ ...
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 ...