In the present paper we have solved the well known Axisymmetric Dirichlet problem for a half-space using the Hankel transform of I-function of one variable. Hankel transform is much effective tool for solving the boundary value problems involving cylindrical coordinates. Here we have considered the Axisymmetric Dirichlet problem for a half-space which is mathematically characterized byBoundary conditions areOur main result is believed to be general and unified in nature. A number of known and new results can be obtained by specializing the coefficients and parameters involved in the kernel.