On a connection between symmetric polynomials, generalized Stirling numbers and the Newton general divided difference interpolation polynomial. (English) Zbl 1043.41005
Summary: 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 \(a_i=i-1\), \(i=1 (1) n\).
MSC:
| 41A10 | Approximation by polynomials |
| 11B73 | Bell and Stirling numbers |
| 05A10 | Factorials, binomial coefficients, combinatorial functions |
| 65D05 | Numerical interpolation |
| 39A05 | General theory of difference equations |
Software:
MapleReferences:
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