Relations among trigonometric functions, Apostol-type numbers and Peters-type Simsek polynomials

GÜN D.

Montes Taurus Journal of Pure and Applied Mathematics, cilt.5, sa.1, ss.90-101, 2023 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 5 Sayı: 1
  • Basım Tarihi: 2023
  • Dergi Adı: Montes Taurus Journal of Pure and Applied Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.90-101
  • Anahtar Kelimeler: Apostol type numbers and polynomials, Changhee numbers, combinatorial numbers and polynomials, generating function, Humbert polynomials, Peters-type Simsek numbers of the first kind, special numbers
  • Akdeniz Üniversitesi Adresli: Evet

Özet

The main purpose of this paper is to derive some new identities and finite sums involving some trigonometric functions, Apostol-type numbers, the Stirling numbers, and two variable Fibonacci polynomials with the aid of generating functions for the Peters-type Simsek numbers and polynomials. We give finite and infinite series representations containing the Peters-type Simsek numbers and polynomials of the first and second kinds. Using trigonometric functions and generating functions, we obtain some formulas relations among the Apostol Bernoulli numbers and polynomials, the Stirling numbers, and the Peters-type Simsek numbers of the first kind. Finally, we introduce some infinite series computational formulas associated with trigonometric functions, the Peters-type Simsek numbers and polynomials, Fibonacci numbers and polynomials, and the Chebyshev polynomials of the second kind.