On the analogs of bernoulli and euler numbers, related identities and zeta and L-functions
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, cilt.45, sa.2, ss.435-453, 2008 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 45 Sayı: 2
- Basım Tarihi: 2008
- Doi Numarası: 10.4134/jkms.2008.45.2.435
- Dergi Adı: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.435-453
- Anahtar Kelimeler: Bernoulli numbers and polynomials, zeta functions
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Akdeniz Üniversitesi Adresli: Evet
Özet
In this paper, by using q-deformed bosonic p-adic integral, we give lambda-Bernoulli numbers and polynomials, we prove Witt's type formula of lambda-Bernoulli polynomials and Gauss multiplicative formula for lambda-Bernoulli polynomials. By using derivative operator to the generating functions of lambda-Bernoulli polynomials and generalized lambda-Bernoulli numbers, we give Hurwitz type lambda-zeta functions and Dirichlet's type lambda-Lfunctions; which are interpolated lambda-Bernoulli polynomials and generalized lambda-Bernoulli numbers, respectively. We give generating function of lambda-Bernoulli numbers with order r. By using Mellin transforms to their function, we prove relations between multiply zeta function and lambda-Bernoulli polynomials and ordinary Bernoulli numbers of order r and lambda-Bernoulli numbers, respectively. We also study on lambda-Bernoulli numbers and polynomials in the space of locally constant. Moreover, we define A-partial zeta function and interpolation function.