TheH-function and temperature in a non-homogeneous bar

Abstract

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.