Computation of the Integer Order Bessel Functions of First Kind with Small Arguments

FENG Jia-ji; JIA Xiao-wei; SHEN Jian-qi

doi:10.3969/j.issn.0372-2112.2016.11.022

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Computation of the Integer Order Bessel Functions of First Kind with Small Arguments

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- Computation of the Integer Order Bessel Functions of First Kind with Small Arguments
- Acta Electronica Sinica Vol. 44, Issue 11, Pages: 2720-2725(2016)
- 作者机构：
  
  上海理工大学理学院,上海,200093
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.NSFC 51476104)
- DOI：10.3969/j.issn.0372-2112.2016.11.022
  CLC： TP301.6
- Published Online：25 November 2016，
  
  Published：2016
- 稿件说明：
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FENG Jia-ji, JIA Xiao-wei, SHEN Jian-qi. Computation of the Integer Order Bessel Functions of First Kind with Small Arguments[J]. Acta Electronica Sinica, 2016, 44(11): 2720-2725.
DOI：

FENG Jia-ji, JIA Xiao-wei, SHEN Jian-qi. Computation of the Integer Order Bessel Functions of First Kind with Small Arguments[J]. Acta Electronica Sinica, 2016, 44(11): 2720-2725. DOI： 10.3969/j.issn.0372-2112.2016.11.022.

摘要

在计算第一类整数阶Bessel函数时，后向递推算法稳定高效.然而，起始点的选取必须有足够高的阶数，并且需要进行归一化处理.本文对Taylor级数展开算法进行研究，并对其级数展开规律、计算精度，以及求和项与参数间的关系进行了讨论.此外，本文利用指数形式，极大扩展了该算法的可计算范围.与du Toit算法、MATLAB和Mathematica应用软件的计算结果比较显示，本文的算法具有较高的准确性和稳定性.

Abstract

Algorithm based on the backward recurrence for computing the integer order Bessel functions of the first kind is stable and efficient.However

the orders of the starting points should be high enough and the normalization is required.In this paper

we introduce an algorithm based on the Taylor series expansion (TSE)

in which all the quantities involved are expressed in the exponential format so as to expand the numeric range of calculation.Comparison against du Toit's algorithm as well as MATLAB and Mathematica shows that our algorithm is stable and reliable.

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Dept.of Electronic Engineering,Tsinghua Univ.

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