The Finite Calculus Associated with Bessel Functions

Abstract

The $\nu$-umbral algebra The $\nu$-umbral field The group of $\nu$-delta functionals under composition Generalized binomial polynomial sequences The composition of polynomial sequences Compositions of Moebius delta functionals Generalized shift invariant operators The generalized derivative of $\nu$-shift invariant operators Generalized Sheffer polynomials Cross sets of polynomials A class of Laguerre type polynomials The generalized heat polynomials A primitive integral for the Euler operator Bernoulli type polynomials and numbers Generalized Euler polynomials and numbers Generalized Stirling numbers and factor polynomials.