Interpretation of the $p$-adic log gamma function and Euler constants using the Bernoulli measure
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چکیده
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Let p be a fixed odd prime number. Throughout this paper Z, Q, Zp, Qp and Cp will respectively denote the ring of rational integers, the field of rational numbers, the ring p-adic rational integers, the field of p-adic rational numbers and the completion of the algebraic closure of Qp. Let vp be the normalized exponential valuation of Cp such that |p|p = p−vp(p) = p−1. If q ∈ Cp, we normally as...
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15 صفحه اولSome Properties and Identities of Bernoulli and Euler Polynomials Associated with p-adic Integral on Zp
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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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1978
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1978-0491622-3