A New Generating Function of (q-) Bernstein-Type Polynomials and Their Interpolation Function

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ŞİMŞEK Y., Acikgoz M.

ABSTRACT AND APPLIED ANALYSIS, cilt.2010, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2010
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1155/2010/769095
  • Dergi Adı: ABSTRACT AND APPLIED ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Akdeniz Üniversitesi Adresli: Evet

Özet

The main object of this paper is to construct a new generating function of the (q-) Bernsteintype polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and derivative of the (q-) Bernstein-type polynomials. We also give relations between the (q-) Bernstein-type polynomials, Hermite polynomials, Bernoulli polynomials of higher order, and the second-kind Stirling numbers. By applying Mellin transformation to this generating function, we define interpolation of the (q-) Bernstein-type polynomials. Moreover, we give some applications and questions on approximations of (q-) Bernstein-type polynomials, moments of some distributions in Statistics.