ABSTRACT
This chapter is entirely devoted for a detailed study of several new classes of wavelet transforms based on certain well-known orthogonal polynomials and special functions. It focuses on the Laguerre and Legendre polynomials and formulate the associated wavelet transforms by employing the tools of Laguerre and Legendre transforms. This is followed by the formulation of another couple of wavelet transforms by using the fundamental notions of the Bessel and Dunkl transforms, which are based on the well-know class of special functions, namely the Bessel and Dunkl functions. The chapter presents a rigorous introduction circumscribing the Bessel functions and the associated Hankel transform. After a sound overview of the Bessel functions, it aims to study the Hankel transform and recall some of its fundamental properties. The chapter is concluded with the exploration of an interesting interface between the classical wavelet transform and the Hartley transform.
