Discrete Gamma (Factorial) Function and Its Series in Terms of a Generalized Difference Operator

Abstract

The recent theory and applications of difference operator ΔL introduced in (M. Maria Susai Manuel et al., 2012) are enriched and extended with a useful tool Δℓ-m[kℓ(n)e-k]||(m-1)ℓ+jk for finding the values of various series of discrete gamma functions in number theory. Illustrative examples show the effectiveness of the obtained results in finding the values of various gamma series.