real analysis - Question about Fourier transform of $e^{-\pi x^2 ...
Jan 17, 2020 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Proving that $\pi(2x) < 2 \pi(x) - Mathematics Stack Exchange
Apr 12, 2016 · In class we proved the prime number theorem, and then proceeded to prove several results such as $\pi(x) = Li(x) +O(x^\theta \ln x)$ and the explicit formula for $\psi_1(x)$. This is clearly quite intuitive but I'm lost as to what I can use to prove the result.
Fourier series for $f(x)=(\pi -x)/2$ - Mathematics Stack Exchange
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Proof that $\\sin(x) > x/2$ - x/2$ - Mathematics Stack Exchange
I need to prove that $\sin(x) > \frac{x}{2}$ if $0<x<\pi/2$ I've started working with the derivative, but if it's possible, I'd rather something simpler than that. Skip to main content Stack Exchange Network
calculus - Let $f (x)=3+x^2+\tan\frac {\pi x}2$, where $-1<x<1
Sep 15, 2020 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Calculate Fourier series of $x(\pi^2-x^2)$ - Mathematics Stack …
A: Fourier series of derivative $\ f'(x) = \pi^{2}-3x^{2}$ The derivative has even parity and will be a sum of cosines.
Show that $\\int\\limits_{-\\infty}^\\infty e^{-\\pi x^2}dx = 1$
Jun 1, 2020 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
integration - Integral of $\sin^2(\pi N x)/(\pi x)^2$ - Mathematics ...
The integral in question is $$ \int_{-\infty}^{\infty} {\sin^2(\pi N x)\over(\pi x)^2}dx = N. \,$$ I'm pretty certain this is true, but I'd like to know if there's a simpler way to solve this than integration by parts, which achieves something along the lines of $$-{\pi x^2\sin(2 \pi N x)\over 4N} +{x\cos(2 \pi Nx)\over4N^2} - \int{\cos(2\pi N ...
integration - $\int_{-\infty}^{\infty}e^{-\pi x^2}\cdot e^{-2\pi ix\xi ...
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
complex analysis - How to prove that $\frac {\sin \pi x} {\pi …
How to prove that $$\frac{\sin \pi x}{\pi x}=\prod_{n=1}^{\infty}\left(1-\frac{x^2}{n^2}\right)$$ I tried it with the Taylor series of $\sin(x)$ but I failed.