Type $\alpha_n$ as alphan

Notes
$\displaystyle\int_0^c rJ_0(r) dr = cJ_1(c)$
In Wolfram alpha, "Solve J0(x) = 0 from 0 to 10" will give the solutions for $J_0(x) = 0$ for $0\leq x\leq 10$.

Problem
A circular membrane with radius $3$ has height u(r,t) at distance r from the center and time t. The membrane has radial symmetry, clamped edges, initial displacement 0, and initial velocity $3$. Then u satisfies the following boundary value problem:




Therefore $u(r,t)=\sum\limits_{n=1}^\infty\left(A_n\cos(a\alpha_nt)+B_n\sin(a\alpha_nt) \right)J_0(\alpha_n r)$ where

n	$\alpha_n$
1
2
3
4

$A_n =$

$\hskip 27pt 2$ ------------------------ $J_1^2\left(3 \alpha_n\right)$

$\displaystyle\int\limits$

$rJ_0\left(\alpha_n r\right)$

dr =

$B_n =$

$\hskip 32pt 2$ ------------------------------ $a\alpha_nJ_1^2\left(3 \alpha_n\right)$

$\displaystyle\int\limits$

$rJ_0\left(\alpha_n r\right)$

dr

$\hskip 17pt$ =

$\hskip 55pt 6$ -------------------------------------------- $J_1\Big($$\Big)$

(see the formula at the top of this problem)

$\displaystyle u(r,t)= \frac{1}{a}\Bigg($

$\hskip 55pt 6$ ------------------------------------------------ $J_1\Big($$\Big)$

$\sin\Big($

$\Big) J_0\Big($

$\Big)$+

$\hskip 57pt$

$\hskip 55pt 6$ ------------------------------------------------ $J_1\Big($$\Big)$

$\sin\Big($

$\Big) J_0\Big($

$\Big)$+

$\hskip 57pt$

$\hskip 55pt 6$ ------------------------------------------------ $J_1\Big($$\Big)$

$\sin\Big($

$\Big) J_0\Big($

$\Big)$+

$\hskip 57pt$

$\hskip 55pt 6$ ------------------------------------------------ $J_1\Big($$\Big)$

$\sin\Big($

$\Big) J_0\Big($

$\Big)+\ldots\Bigg)$