On a connection between symmetric polynomials, generalized Stirling numbers and the Newton general divided difference interpolation polynomial

Abstract

This paper gives a connection between symmetric polynomials, generalized Stirling numbers and the Newton general divided difference interpolation polynomial. The generalized Stirling numbers of the first and second kind denoted s n, k [ a] and S n, k [ a] respectively are given symbolically for the case n=5, as an illustrative example, by using MAPLE programming [MAPLE V R3 Programming Reference Manual]. These numbers depend on n, k and n distinct values a 1, a 2,…, a n . The ordinary Stirling numbers s n, k and S n, k may be obtained as special cases by taking a i = i−1, i=1 (1) n .