Use of generalized Taylor series expansion

Presents a class of orthonormal basis functions which is based on a generalization of the Taylor series expansion. Several examples are given showing the capabilities of this class of expansion for applications in exponential approximation. The generalized Taylor series expansion (known as the Bürmann series) is also shown to be useful in representing dilated and translated versions of a signal with little error using a single function. The Bürmann expansion is also shown to be useful in providing an alternative approach to the wavelet and Gabor transform. It is more efficient than the ordinary power series in small term approximations to exponential signals