A note on the Bernoulli and Euler polynomials
نویسندگان
چکیده
منابع مشابه
On Identities Involving Bernoulli and Euler Polynomials
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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where J5m(x), Em(x) denote the polynomials of Bernoulli and Euler in the usual notation. It is perhaps not so familiar that (1.1) and (1.2) characterize the polynomials. More precisely, as Nielsen has pointed out [3, p. 54], if a normalized polynomial satisfies (1.1) for a single value k>l, then it is identical with Bm(x); similarly if a normalized polynomial satisfies (1.2) for a single odd k>...
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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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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2003
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(03)80058-7