ABSTRACT
Given a Sturm–Liouville operator on an interval of the real line, it is well known that its eigenfunction expansion gives rise to an integral transform which shares many properties with the ordinary Fourier transform [18,52]. Since various standard special functions are solutions of Sturm–Liouville equations, the class of integral transforms of Sturm–Liouville type includes, as particular cases, many common integral transforms (Hankel, Kontorovich–Lebedev, Mehler–Fock, Jacobi, Laguerre, etc.).
