On Combinatorial Numbers and Polynomials and Their Applications

ŞİMŞEK Y.

International Conference on Numerical Analysis and Applied Mathematics 2021, ICNAAM 2021, Rhodes, Yunanistan, 20 - 26 Eylül 2021, cilt.2849 identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 2849
  • Doi Numarası: 10.1063/5.0162213
  • Basıldığı Şehir: Rhodes
  • Basıldığı Ülke: Yunanistan
  • Anahtar Kelimeler: Array polynomials, B-Spline, Binomial coefficients, Eulerian spline, Frobenius-Euler numbers and polynomials, Functional equations, Generating function, Special numbers and polynomials
  • Akdeniz Üniversitesi Adresli: Evet

Özet

The aim of this study is to define a higher-order extension of the numbers arising from the finite sums containing higher powers of binomial coefficients. By using functional equations of the generating functions for these numbers, we derive some identities and relations between these numbers and λ-array polynomials. Finally, we give some remarks and observations on relations among the aforementioned numbers, λ-array polynomials and Eulerian type splines with their applications.