Chapter 11.6, Problem 18P

Determine the Fourier-Bessel expansion in the functions $J_0\left({\text{λ}}_{k}x\right)$ for $f\left(x\right)=x^2$, on the interval $\left(0,1\right)$. [Here the ${\text{λ}}_k$ denotes the positive zeros of $J_0\left(x\right)$.