Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and p-adic q-integrals

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Simsek Y.

TURKISH JOURNAL OF MATHEMATICS, cilt.42, sa.2, ss.557-577, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1703-114
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.557-577
  • Anahtar Kelimeler: Generalized Bernoulli numbers and polynomials, generalized Euler numbers and polynomials, Apostol- Bernoulli and Apostol-Euler numbers and polynomials, Daehee numbers and polynomials, Stirling numbers, generating function, Dirichlet character, p-adic Volkenborn integral, Q-BERNOULLI NUMBERS, EULER NUMBERS, IDENTITIES, EXTENSION, ANALOGS, ZETA
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, by applying the p-adic q-integrals to a family of continuous differentiable functions on the ring of p-adic integers, we construct new generating functions for generalized Apostol-type numbers and polynomials attached to the Dirichlet character of a finite abelian group. By using these generating functions with their functional equations, we derive various new identities and relations for these numbers and polynomials. These results are generalizations of known identities and relations including some well-known families of special numbers and polynomials such as the generalized Apostol-type Bernoulli, the Apostol-type Euler, the Frobenius-Euler numbers and polynomials, the Stirling numbers, and other families of numbers and polynomials. Moreover, by the help of these generating functions, we also construct other new families of numbers and polynomials with their generating functions. By using these functions, we investigate some fundamental properties of these numbers and polynomials. Finally, we also give explicit formulas for computing the Apostol-Bernoulli and Apostol-Euler numbers.