Novel formulas of moments of Negative Binomial distribution connected with Apostol-Bernoulli numbers of higher order and Stirling numbers

Simsek B.

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, cilt.118, sa.4, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 118 Sayı: 4
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s13398-024-01640-w
  • Dergi Adı: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Anahtar Kelimeler: 05A10, 05A15, 11B68, 60E05, Apoostol Bernoulli numbers and polynomials of higher order, Binomial coefficients, Moment generating function, Negative Binomial distribution, Probability distribution, Stirling numbers
  • Akdeniz Üniversitesi Adresli: Evet

Özet

The main subject of this article is to present and reveal some new relationships between the moment generating functions of the Negative Binomial distribution and the generating functions for the Apostol-Bernoulli numbers and polynomials. By the help of these relations and Binomial series, we derive many computation formulas. These formulas give relations among moments, factorial moments, and the Apostol-Bernoulli numbers and polynomials, the Stirling numbers, and also other special functions related to zeta functions. By using these formulas, we give some numerical values of moments, expected value, and variance. Finally, we give some observations on formulas for the moments involivin binomial series and zeta functions.