Euler polynomials, Bernoulli polynomials, and Lévyʼs stochastic area formula
نویسندگان
چکیده
منابع مشابه
A new class of generalized Bernoulli polynomials and Euler polynomials
The main purpose of this paper is to introduce and investigate a new class of generalized Bernoulli polynomials and Euler polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the Srivastava–Pintér addition theorem is obtained. We give new identities involving q-Bernstein polynomials.
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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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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: Bulletin des Sciences Mathématiques
سال: 2011
ISSN: 0007-4497
DOI: 10.1016/j.bulsci.2011.07.009