Expansions in terms of generalized telegraph polynomials and complementry function

Abstract

Two sets of particular solutions. the genaeralized telegraph polynomials and thye compplementary functions, are constructed for the generalized telegraph equation.Theor relations with the generlized heat polynomialks and the rdial wave polynomials are established. From their asymptotic estimates, we obtain sufcient conditions for the convergence of the series om terms of terms of these functions certain initial value pronlems can be solved in series in series of these of these funtions.

Keywords:

• Generalized telegraph polynomials
• complementary functions
• growth condition
• asymptotic