SYMMETRIC IDENTITIES FOR CARLITZ-TYPE TWISTED $(h,q)$-BERNOULLI NUMBERS AND POLYNOMIALS ASSOCIATED WITH $p$-ADIC $q$-INTEGRAL ON $\mathbb{Z}_p$
نویسندگان
چکیده
منابع مشابه
Multivariate Twisted p-Adic q-Integral on Zp Associated with Twisted q-Bernoulli Polynomials and Numbers
Let p be a fixed prime number. Throughout this paper, the symbols Z,Zp,Qp,C, and Cp will denote the ring of rational integers, the ring of p-adic integers, the field of p-adic rational numbers, the complex number field, and the completion of the algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z N ∪ {0}. Let vp be the normalized exponential valuation of Cp with |p|...
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and Applied Analysis 3 2. Some Identities of Bernoulli and Euler Polynomials By 1.4 , we get Ek ( x y ) k ∑ j 0 ( k j ) yk−jEj x , for ∈ Z . 2.1 From 2.1 , we note that Ek ( x y ) k ∑ j 0 ( k j ) yk−jEj x y k ∑ j 1 k j ( k − 1 j − 1 ) yk−jEj x . 2.2 Thus, we have k−1 ∑ j 0 ( k − 1 j ) yk−1−j Ej 1 x j 1 Ek ( x y ) − y k . 2.3 Replacing k by k 1 in 2.3 , we obtain the following proposition. Propo...
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Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper we introduce the twisted (h, q)-tangent numbers T (h) n,q,w and polynomials T (h) n,q,w (x). Some interesting results and relationships are obtained.
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ژورنال
عنوان ژورنال: International Journal of Pure and Apllied Mathematics
سال: 2016
ISSN: 1311-8080,1314-3395
DOI: 10.12732/ijpam.v110i2.13