A new type of Taylor series expansion.

IF 1.6 3区数学 Q1 Mathematics

Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-05-15 DOI:10.1186/s13660-018-1709-8

Mohammad Masjed-Jamei, Zahra Moalemi, Iván Area, Juan J Nieto

引用次数: 7

Abstract

We present a variant of the classical integration by parts to introduce a new type of Taylor series expansion and to present some closed forms for integrals involving Jacobi and Laguerre polynomials, which cannot be directly obtained by usual symbolic computation programs, i.e., only some very specific values can be computed by the mentioned programs. An error analysis is given in the sequel for the introduced expansion.

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一类新的泰勒级数展开式。

本文提出了经典分部积分的一种变体，引入了一种新的泰勒级数展开式，并给出了涉及Jacobi多项式和Laguerre多项式的积分的一些封闭形式，这些形式是通常的符号计算程序不能直接得到的，即只有一些非常特定的值可以通过上述程序计算出来。在续文中对引入的展开进行了误差分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Inequalities and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.30

自引率

6.20%

发文量

136

审稿时长

3 months

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.