# Tagged Questions

**9**

votes

**1**answer

243 views

### Is a Bessel function larger than all other Bessel functions when evaluated at its first maximum?

Let $\mathcal{J}_{n+1/2}$ be the Bessel function of order $n+1/2$. Let $x_n$ denote the first zero of its derivative, which is also the location of the first maximum of $\mathcal{J}_{n+1/2}$.
My ...

**11**

votes

**1**answer

304 views

### Is there something wrong with Hörmander's theorem on stationary phase method

It is well-know that the Bessel function has the asymptotic expansion $J_n(\omega) \sim \left( \frac 2 {\pi \omega} \right)^{1/2} \left( \cos \left(\omega -\frac 1 2 n \pi - \frac 1 4 \pi\right) - ...

**1**

vote

**0**answers

183 views

### An integral with Gamma functions (Part 2)

I was wondering if there is a generalization of the integral discussed here to a case like,
\begin{equation}\int \frac{d^dq}{q^{\nu_1}\vert \vec{q} \pm \vec{k}_1\vert ^{\nu_2}\vert \vec{q} \pm ...

**27**

votes

**7**answers

2k views

### How should an analytic number theorist look at Bessel functions?

(And a related question: Where should an analytic number theorist learn about Bessel functions?)
Bessel functions occur quite frequently in analytic number theory. One example, Corollary 4.7 of ...

**3**

votes

**1**answer

571 views

### Fourier and Bessel

Oliver Heaviside, on page 387 of Electrical Papers, Vol. I, Macmillan and Co., 1892, available here, writes
$$v = 1 - \frac{n^2r^2}{2^2} + \frac{n^4r^4}{2^2 4^2} - \frac{n^6r^6}{2^24^26^2} + \ldots ...

**0**

votes

**3**answers

706 views

### How to isolate $f(x)$ in $f(x+a)=f(x)+a\times g(x)$?

$a \in \mathbb{R}$
$f:\mathbb{R} \rightarrow \mathbb{R}$
$g:\mathbb{R} \rightarrow \mathbb{R}$
For generic functions $f$ and $g$, how isolate $f(x)$ in the equation below?
$f(x+a)=f(x)+a\times ...