Newton's Generalised Binomial theorem states that if $\ x\ $ and $\ y\ $ are real numbers with $\ \vert x \vert > \vert y \vert\ (\text{note that } \left\vert \frac{y}{x} \right\vert < 1),\ $ and $\ r\ $ is any complex number, one has
$$ (x+y)^r = \sum_{k=0}^{\infty} \binom{r}{k} x^{r-k} y^k = x^...
I am currently reading Fourier Analysis and its applications by Gerald B. Folland.
In Chapter 7, there is the following equation:
\begin{align}
\int_{-\infty}^{\infty} e^{i \xi(x-y)} e^{-\varepsilon^{2} \cdot \frac{\xi^2}{2}}\, d \xi \nonumber
&=\mathcal{F}\left\{e^{-\epsilon^{2} \cdot \frac{\...
I am currently reading Fourier Analysis and its applications by Gerald B. Folland.
In Chapter 7, there is the following equation:
\begin{align}
\int_{-\infty}^{\infty} e^{i \xi(x-y)} e^{-\varepsilon^{2} \cdot \frac{\xi^2}{2}}\, d \xi \nonumber
&=\mathcal{F}\left\{e^{-\epsilon^{2} \cdot \frac{\...
