A Note on Characteristic Function for Bernstein Polynomials Involving Special Numbers and Polynomials

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Simsek B.

FILOMAT, vol.34, no.2, pp.543-549, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.2298/fil2002543s
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.543-549
  • Keywords: Bernstein polynomials, Generating function, Expected values, Moment generating function, Characteristic function, Distribution functions, Combinatorial numbers, Stirling numbers, GENERATING-FUNCTIONS, BERNOULLI, EULER
  • Akdeniz University Affiliated: Yes

Abstract

The aim of this present paper is to establish and study generating function associated with a characteristic function for the Bernstein polynomials. By this function, we derive many identities, relations and formulas relevant to moments of discrete random variable for the Bernstein polynomials (binomial distribution), Bernoulli numbers of negative order, Euler numbers of negative order and the Stirling numbers.