The Families of L-Series Associated with Decomposition of the Generating Functions
FILOMAT, cilt.30, sa.7, ss.1789-1799, 2016 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 30 Sayı: 7
- Basım Tarihi: 2016
- Doi Numarası: 10.2298/fil1607789a
- Dergi Adı: FILOMAT
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1789-1799
- Anahtar Kelimeler: q-Frobenius-Euler polynomials, q-series, Generating functions, Dirichlet L-function, Hurwitz zeta function, Riemann zeta function, Mellin transformation, ZETA, POLYNOMIALS, EULER, NUMBERS, EXTENSIONS, BERNOULLI
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Akdeniz Üniversitesi Adresli: Evet
Özet
By using periodic functions from the nonnegative integers to the complex numbers, we generalize the generating function of the q-Apostol type Eulerian polynomials and numbers attached the character defined in [1]. Then using this generating function, we a construct new L-type series. By using periodic functions, we derive decomposition of the generating functions for the q-Euler numbers and polynomials. Applying the Mellin transformation to the decomposition of the generating functions, we introduce and investigate the various properties of a certain new family of the Dirichlet type L-series and the Dirichlet L-function. Finally, we derive many potentially useful results involving these functions polynomials and numbers.