New identities involving Bernoulli, Euler and Genocchi 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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Using the finite difference calculus and differentiation, we obtain several new identities for Bernoulli and Euler polynomials; some extend Miki’s and Matiyasevich’s identities, while others generalize a symmetric relation observed by Woodcock and some results due to Sun.
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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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Guodong Liu Department of Mathematics, Huizhou University, Huizhou, Guangdong 516015, China Correspondence should be addressed to Guodong Liu, [email protected] Received 18 June 2009; Accepted 12 August 2009 Recommended by Leonid Berezansky An explicit formula, the generalized Genocchi numbers, was established and some identities and congruences involving the Genocchi numbers, the Bernoul...
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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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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2013
ISSN: 1687-1847
DOI: 10.1186/1687-1847-2013-74