Sums of finite products of Legendre and Laguerre polynomials

被引：0
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作者：
Taekyun Kim
Dae San Kim
Dmitry V. Dolgy
Jin-Woo Park
机构：
[1] Kwangwoon University,Department of Mathematics
[2] Sogang University,Department of Mathematics
[3] Kwangwoon University,Hanrimwon
[4] Daegu University,Department of Mathematics Education
来源：
Advances in Difference Equations | / 2018卷
关键词：
Fourier series; Finite products; Legendre polynomials; Laguerre polynomials; Bernoulli polynomials; Euler polynomials; 11B68; 33C45; 42A16;
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摘要：
In this paper, we study sums of finite products of Legendre and Laguerre polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we are going to express those sums of finite products as linear combinations of Bernoulli polynomials. Further, by using a method other than Fourier series expansions, we will be able to express those sums in terms of Euler polynomials.
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