ABSTRACT
This chapter deals with Jacobi and Gegenbauer transforms and their basic operational properties. The former is a fairly general finite integral transform in the sense that both Gegenbauer and Legendre transforms follow as special cases of the Jacobi transform. Some applications of both Jacobi and Gegenbauer transforms are discussed. This chapter is based on papers by Debnath (1963, 1967), Scott (1953), Conte (1955), and Lakshmanarao (1954). In Chapters 12-15, we discussed several special transforms with orthogonal polynomials as kernels. All these special transforms have been unified by Eringen (1954) in his paper on the finite Sturm-Liouville transform.
