Some Identities of Symmetry for the Generalized Bernoulli Numbers and Polynomials
نویسندگان
چکیده
and Applied Analysis 3 2. Symmetry of Power Sum and the Generalized Bernoulli Polynomials Let χ be the Dirichlet character with conductor d ∈ N. From 1.3 , we note that ∫ X χ x edx t ∑d−1 i 0 χ i e it edt − 1 ∞ ∑ n 0 Bn,χ t n! , 2.1 where Bn,χ x are the nth generalized Bernoulli numbers attached to χ. Now, we also see that the generalized Bernoulli polynomials attached to χ are given by ∫ X χ ( y ) e x y dy t ∑d−1 i 0 χ i e it edt − 1 e xt ∞ ∑ n 0 Bn,χ x t n! . 2.2 By 2.1 and 2.2 , we easily see that ∫
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