Fourier expansions for Genocchi polynomials of higher order
نویسندگان
چکیده
منابع مشابه
Fourier Expansions and Integral Representations for Genocchi Polynomials
In this paper, by using the Lipschitz summation formula, we obtain Fourier expansions and integral representations for the Genocchi polynomials. Some other new and interesting results are also shown.
متن کامل-Genocchi Polynomials and Numbers of Higher Order
Copyright q 2010 Lee-Chae Jang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate several arithmetic properties of h, q-Genocchi polynomials and numbers of higher order.
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We find Fourier expansions of Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. We give a very simple proof of them.
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where we use the technical method’s notation by replacing G x by Gn x , symbolically, see 1, 2 . In the special case x 0, Gn Gn 0 are called the nth Genocchi numbers. From the definition of Genocchi numbers, we note that G1 1, G3 G5 G7 · · · 0, and even coefficients are given by G2n 2 1 − 22n B2n 2nE2n−1 0 see 3 , where Bn is a Bernoulli number and En x is an Euler polynomial. The first few Gen...
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In this paper, we consider the Riesz transform of higher order associated with the harmonic oscillator [Formula: see text], where Δ is the Laplacian on [Formula: see text]. Moreover, the boundedness of Riesz transforms of higher order associated with Hermite functions on the Hardy space is proved.
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ژورنال
عنوان ژورنال: Journal of Mathematics and Computer Science
سال: 2020
ISSN: 2008-949X
DOI: 10.22436/jmcs.022.01.06