FORMULAS DERIVED FROM MOMENT GENERATING FUNCTIONS AND BERNSTEIN POLYNOMIALS

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Simsek B.

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, vol.13, no.3, pp.839-848, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.2298/aadm191227036s
  • Journal Name: APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.839-848
  • Keywords: Special polynomials and numbers, Generating functions, Array polynomials, Stirling numbers, Moment generating function, Characteristic functions, Distribution functions, Binomial coefficients, Combinatorial identities, BERNOULLI
  • Open Archive Collection: AVESIS Open Access Collection
  • Akdeniz University Affiliated: Yes

Abstract

The purpose of this paper is to provide some identities derived by moment generating functions and characteristics functions. By using functional equations of the generating functions for the combinatorial numbers y(1) (m; n; lambda), defined in [12, p. 8, Theorem 1], we obtain some new formulas for moments of discrete random variable that follows binomial (Newton) distribution with an application of the Bernstein polynomials. Finally, we present partial derivative formulas for moment generating functions which involve derivative formula of the Bernstein polynomials.