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.