A note on high order Bernoulli numbers and polynomials using differential equations
نویسندگان
چکیده
منابع مشابه
A note on q-Bernoulli numbers and polynomials
By using q-integration, we will give some integral equation which are related to the Barnes’ multiple Bernoulli numbers. The object of this paper is to give explicit q-integral’s formulae which are related to Barnes’ multiple q-Bernoulli polynomials. §
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Abstract Recently, B. A. Kupershmidt have constructed a reflection symmetries of q-Bernoulli polynomials (see [9]). In this paper we give another construction of a q-Bernoulli polynomials, which form Barnes’ multiple Bernoulli polynomials at q = 1, cf. [1, 13, 14]. By using q-Volkenborn integration, we can also investigate the properties of the reflection symmetries of these’ q-Bernoulli polyno...
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ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2014
ISSN: 0096-3003
DOI: 10.1016/j.amc.2014.10.074