Yayın: A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials
Tarih
Kurum Yazarları
Özden, Hacer
Yazarlar
Şimşek, Yılmaz
Srivastava, Hari M.
Danışman
Dil
Türü
Yayıncı:
Pergamon-Elsevier Science
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Özet
The goal of this paper is to unify and extend the generating functions of the generalized Bernoulli polynomials, the generalized Euler polynomials and the generalized Genocchi polynomials associated with the positive real parameters a and b and the complex parameter beta. By using this generating function, we derive recurrence relations and other properties for these polynomials. By applying the Mellin transformation to the generating function of the unification of Bernoulli, Euler and Genocchi polynomials, we construct a unification of the zeta functions. Furthermore, we give many properties and applications involving the functions and polynomials investigated in this paper.
Açıklama
Kaynak:
Anahtar Kelimeler:
Konusu
Bernoulli numbers and Bernoulli polynomials, Euler numbers and Euler polynomials, Genocchi numbers and Genocch polynomials, Riemann and Hurwitz (or generalized) zeta functions, Hurwitz-Lerch zeta function, Lerch zeta function, Polylogarithm function, Lipschitz-Lerch zeta function, Recurrence relations, Mellin transformation, Dirichlet character, Apostol-bernoulli, Zeta, Numbers, Extension, Formulas, Mathematics, Function evaluation, Functions, Polynomials, Bernoulli polynomials, Dirichlet characters, Euler numbers, Lerch zeta function, Mellin transformation, Polylogarithm functions, Recurrence relations, Zeta function, Number theory
Alıntı
Özden, H. vd. (2010). "A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials". Computers & Mathematics with Applications, 60(10), 2779-2787.