10.9 Back to our initial problem

After all that we have learned, we know that in order to determine the solution of the initial problem in Sec. 10.1 we would have to calculate the integrals

{A}_{j} = {2\over { c}^{2}{J}_{1}^{2}(c{α}_{j})}{\mathop{\mathop{\mathop{∫ }\nolimits }}\nolimits }_{0}^{c}f(ρ){J}_{ 0}({α}_{j}ρ)ρdρ
(10.86)