I have a heat transfer down a cylindrical pipe problem that I am running into issues solving. I separated the PDE into a Sturm-Liouville eigenvalue problem. One side solves down to this: R(η) = C1 BesselJ0 (η√("λ" )) + C2 BesselY0 (η√("λ" )) I plugged in the boundary conditions of R(1)=0 and R'(0)=0. R' contains C2 BesselY1(0) and since BesselY1(0) has no solution, C2 must equal zero. Applying the second boundary condition gives us this: BesselJ0 (√(λ)) = 0 I'm not entirely sure how to solve this though. Is there an inverse Bessel function similar to sin-1? Thanks in advance.