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a = 1;
c = 0.5;
f[r_] := a^2 - r^2
g[r_] := 0
x0[m_] := N[BesselJZero[0, m]]
k[m_] := x0[m]/a
\[Omega][m_] := c*k[m]
A[m_] := (2 \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(a\)]\(r*
BesselJ[0, k[m]*r]\ *f[r] \[DifferentialD]r\)\))/(
a^2*BesselJ[1, x0[m]]^2)
B[m_] := (2 \!\(
\*Subsuper...