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

  • Authors:

  • Moawwad El-Mikkawy;Beih El-Desouky

  • Affiliations:

  • Department of Mathematics, Faculty of Science Mansoura University, Mansoura 35516, Egypt;Department of Mathematics, Faculty of Education, Suez Canal University, Port Said, Egypt

  • Venue:
  • Applied Mathematics and Computation
  • Year:
  • 2003

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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 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, i = 1(1)n.