TheH-function and temperature in a non-homogeneous bar

We employ theH-function in obtaining the formal solution of the partial differential equation $$frac{{partial v}}{{partial t}} = lambda frac{partial }{{partial u}}left[ {(1 - u^2 )frac{{partial v}}{{partial t}}} right]$$ related to a problem of heat conduction by making use of the integral and orthogonality property of the Jacobi polynomials. The result generalizes a number of known particular case on specialization of the parameters.