Abstract
In this paper a complete orthonormal family of Laguerre-Bessel functions is derived and certain spaces of testing functions and generalized functions are defined, whose members can be expressed in terms of a Fourier-Laguerre-Bessel series, which gives the inversion formula for Laguerre-Finite Hankel transform of generalized functions. The convergence of the series is interpreted in the weak distributional sense. An operational transform formula is derived which together with the inversion formula is applied in solving certain distributional differential equations. AMS Subject Classification: 44F12,44A15,46F10,41A58.
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