FORMULAS DERIVED FROM MOMENT GENERATING FUNCTIONS AND BERNSTEIN POLYNOMIALS

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Simsek B.

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, cilt.13, sa.3, ss.839-848, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.2298/aadm191227036s
  • Dergi Adı: APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.839-848
  • Anahtar Kelimeler: Special polynomials and numbers, Generating functions, Array polynomials, Stirling numbers, Moment generating function, Characteristic functions, Distribution functions, Binomial coefficients, Combinatorial identities, BERNOULLI
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.