A new type of Taylor series expansion

机译：新型泰勒级数展开

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摘要

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.

机译：我们介绍了经典积分的一种变体，以介绍一种新型的泰勒级数展开式，并给出涉及Jacobi和Laguerre多项式的积分的某些闭合形式，这些形式不能通过常规的符号计算程序直接获得，即仅某些非常特殊的值可以由上述程序计算。对引入的扩展进行了后续的错误分析。

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期刊名称 Springer Open Choice
作者
Mohammad Masjed-Jamei; Zahra Moalemi; Iván Area; Juan J. Nieto;
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作者单位

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年(卷),期 -1(2018),1
年度 -1
页码 116
总页数 10
原文格式 PDF
正文语种
中图分类外科学;
关键词
Generalized Taylor expansion Integration by parts Integral remainder Error bound Jacobi and Laguerre polynomials;

机译：广义泰勒展开;部分积分;余数积分;误差界;Jacobi和Laguerre多项式;

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专利

1. A new type of Taylor series expansion [J] . Mohammad Masjed-Jamei, Zahra Moalemi, Iván Area, Journal of inequalities and applications . 2018,第1期

机译：新型泰勒级数展开
2. Leveraged {ETF} Implied Volatilities, Family Of Density Expansions For Lévy-Type Processes, Taylor Series Approach To Pricing And Implied Vol For LSV Models, Complete Duality For Martingale Optimal Transport, Network Filtering, Robust Dynkin Game, Chebysh [J] . K.N.P. Kumar Advances in Physics Theories and Applications . 2013,第3期

机译：杠杆{ETF}隐含波动率，Lévy型过程的密度扩展族，泰勒级数定价方法和LSV模型的隐含波动率，Mar最佳运输的完全对偶性，网络过滤，鲁棒的Dynkin博弈，Chebysh
3. The expansion in series (of taylor types) of (k - 1) derivative of Dirac's delta in m~2 + P [J] . Aguirre T. Manuel A Integral transforms and special functions . 2003,第2期

机译：Diracδ的（k-1）导数在（m〜2 + P）中的（泰勒类型）级数展开
4. Taylor Series Expansion with the Fluctuation Freely Approximated Remainder over Gauss Wave Type Basis Functions [C] . Caner Gulpinar, Meseret Tuba Gulpinar, Metin Demiralp International Conference of Computational Methods in Sciences and Engineering . 2014

机译：泰勒串联扩展与波动自由近似于高斯波型基本函数
5. Floating-point unit design using Taylor-series expansion algorithms. [D] . Kwon, Taek-Jun. 2009

机译：使用泰勒级数展开算法的浮点单元设计。
6. Zipf’s Heaps’ and Taylor’s Laws are Determined by the Expansion into the Adjacent Possible [O] . Francesca Tria, Vittorio Loreto, Vito D. P. Servedio 2018

机译：ZIPF的堆积和泰勒的法律是由扩展到相邻的
7. An integral expansion for analytic functions based upon the remainder values of the Taylor series expansions [O] . Masjed-Jamei Mohammad, Srivastava H.M. 2009

机译：基于泰勒级数展开式余数的解析函数的积分展开式
8. Taylor series expansion and modified extended Prony analysis for localization [R] . Mosher, J. C., Lewis, P. S. 1994

机译：泰勒级数展开和改进的扩展prony分析用于定位

A new type of Taylor series expansion

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