How to define the solution for the Helmholtz problem

Questions
1

The following expression

u_{nm}(r,\theta)=J_n(x_{nm}\frac{r}{a}) \begin{cases} \cos n \theta, & n=0,1,2 , m=1,2 \\ \sin n \theta, & \end{cases}

gives the solution for the Helmholtz problem. On the circular disc with center 0 and radius a. For a = 1, the plot in 3-dimensional graphics of the solutions on Mathematica for (n,m)=(2,2) and (n,m)=(0,2) and then calculate the eigenfunction

k_{nm}= \frac{x_{nm}}{a}

My problem is that I don’t know how to define the function of the solution on Mathematica

a = 1; (* Set the value of a *)
n = 2; (* Set the value of n *)
m = 2; (* Set the value of m *) 
x[n_,m_] := N[BesselJ[n, m]]
k[n,m_] := x[n,m]/a
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