Relations Arising From A Family Of Combinatorial Numbers And Bernstein Type Basis Functions

Kucukoglu I., ŞİMŞEK Y.

International Conference of Numerical Analysis and Applied Mathematics (ICNAAM), Thessaloniki, Yunanistan, 25 - 30 Eylül 2017, cilt.1978 identifier identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 1978
  • Doi Numarası: 10.1063/1.5043694
  • Basıldığı Şehir: Thessaloniki
  • Basıldığı Ülke: Yunanistan
  • Anahtar Kelimeler: Bernstein basis functions, generating functions, functional equations, special numbers, special functions, combinatorial identity, combinatorial sum, binomial coefficients, gamma function, beta function
  • Akdeniz Üniversitesi Adresli: Evet

Özet

The aim of this paper is to give some combinatorial sums, identities and relations related to a family of combinatorial numbers and the Bernstein type basis functions. With the help of generating functions for the combinatorial numbers from this aforementioned family, we give some functional equations. By using these functional equations, we obtain several relationships including these combinatorial numbers and the Bernstein type basis functions. Moreover, we provide not only some identities, but also applications including combinatorial sums, integrals, the combinatorial numbers, the extended Bersntein basis functions, and the beta function.