Some Identities on the Generalizedq-Bernoulli,q-Euler, andq-Genocchi Polynomials
نویسندگان
چکیده
منابع مشابه
Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials
In 2008, Liu and Wang established various symmetric identities for Bernoulli, Euler and Genocchi polynomials. In this paper, we extend these identities in a unified and generalized form to families of Hermite-Bernoulli, Euler and Genocchi polynomials. The procedure followed is that of generating functions. Some relevant connections of the general theory developed here with the results obtained ...
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Let p be a fixed odd prime number. Throughout this paper, Zp, Qp and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers and N = N ∪ {0}. The p-adic norm is normally defined by |p|p = 1/p. As an indeterminate, we assume that q ∈ Cp with |1 − q|p < 1 (see [1-43]...
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and Applied Analysis 3 If n ∈ Nwith n ≡ 0 mod 2 , then we have I−1 fn − I−1 f 2 n−1 ∑ l 0 −1 l−1f l . 2.6 From 1.4 and 2.3 , we derive ∫ Zp eqdμ−1 x 2 2 q 1 − −q −1 et − −q −1 2 2 q ∞ ∑ n 0 Hn −q−1 t n n! . 2.7 Thus, we note that ∫ Zp xqdμ−1 x 2 2 q Hn −q−1 , ∫ Zp y x qdμ−1 x 2 2 q Hn −q−1, x . 2.8 Let n ∈ N with n ≡ 1 mod 2 . Then we obtain 2 q n−1 ∑ l 0 −1 ql qHm −q−1, n Hm −q−1 . 2.9 For n ∈...
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Let p be a fixed odd prime number. Throughout this paper, we always make use of the following notations: Z denotes the ring of rational integers, Zp denotes the ring of padic rational integer, Qp denotes the ring of p-adic rational numbers, and Cp denotes the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z N {0}. Let Cpn {ζ | ζpn 1} be the cyclic g...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2013
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2013/293532