  We derive sufficient conditions for the existence of the Weber formal
solution of the corresponding integral equation, related to the familiar
Weber-Orr integral transforms. This gives a solution to the old
Weber-Titchmarsh problem (posed in Proc. Lond. Math. Soc. 22(2) (1924), pp.15,
16.) Our method involves properties of the inverse Mellin transform of
integrable functions. The Mellin-Parseval equality and some integrals with the
associated Legendre functions are used.
