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

Yilmaz ŞİMŞEK

Makale detayları

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

Yazarlar:

Yilmaz ŞİMŞEK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 2, pp.557-577

Belge Tipi:

Makale

Yayın Tarihi:

3/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745916

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

In this paper, by applying the ppp-adic qqq-integrals to a family of  continuous differentiable functions on the ring of ppp-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.

Makale detayları

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

Yazarlar: Yilmaz ŞİMŞEK

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2018 Vol.42 Issue 2, pp.557-577

Belge Tipi: Makale

Yayın Tarihi: 3/2018

Belge Dili: Türkçe

Document ID (Org No.): 2000745916

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Yilmaz ŞİMŞEK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 2, pp.557-577

Belge Tipi:

Makale

Yayın Tarihi:

3/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745916

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098