ON A GENERALIZED FUNCTION-TO-SEQUENCE TRANSFORM

Abstract

By attaching a sequence (Formula presented) to the binomial transform, a new operator (Formula presented) is obtained. We use the same sequence to define a new transform (Formula presented) mapping derivatives to the powers of (Formula presented), and integrals to (Formula presented). The inverse transform (Formula presented) of (Formula presented) is introduced and its properties are studied. For α = (−1) , (Formula presented) reduces to the Borel transform. Applying (Formula presented) to Bessel’s differential operator (Formula presented), we obtain Bessel’s discrete operator (Formula presented). Its eigenvectors correspond to eigenfunctions of Bessel’s differential operator. n n