Some Identities on Bernoulli and Euler Numbers
نویسندگان
چکیده
منابع مشابه
Arithmetic Identities Involving Bernoulli and Euler Numbers
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. The p-adic norm is normalized so that |p|p 1/p. Let N be the set of natural numbers and Z N ∪ {0}. Let UD Zp be the space of uniformly differentiable functions on Zp. For f ∈ ...
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Let p be a fixed odd prime. Throughout this paper, Zp,Qp,Cp will, respectively, denote the ring of p-adic integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp. The p-adic absolute value | |p on Cp is normalized so that |p|p 1/p. Let Z>0 be the set of natural numbers and Z≥0 Z>0 ∪ {0}. As is well known, the Bernoulli polynomials Bn x are defined by the ge...
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A class of identities satisfied by both Bernoulli and Euler polynomials is established. Recurrence relations for Bernoulli and Euler numbers are derived.
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We establish two general identities for Bernoulli and Euler polynomials, which are of a new type and have many consequences. The most striking result in this paper is as follows: If n is a positive integer, r + s + t = n and x + y + z = 1, then we have r s t x y n + s t r y z n + t r s z x n = 0 where s t x y n := n k=0 (−1) k s k t n − k B n−k (x)B k (y). It is interesting to compare this with...
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ژورنال
عنوان ژورنال: Discrete Dynamics in Nature and Society
سال: 2012
ISSN: 1026-0226,1607-887X
DOI: 10.1155/2012/486158