On certain summation problems and generalizations of Eulerian polynomials and numbers

摘要

The main purpose of this paper is to introduce two kinds of generalized Eulerian polynomials and numbers which are associated with the constructions of certain summation formulas for extended arithmetic-geometric series. Also we present some basic formulas related to certain generalized Eulerian numbers, Carlitz-Howard's degenerated Stirling numbers and Dickson-Stirling numbers.