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

摘要

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 sn,k[a] and Sn,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 a1,a2,…,an. The ordinary Stirling numbers sn,k and Sn,k may be obtained as special cases by taking ai=i−1, .