贝塞尔函数
计算
数学
傅里叶变换
高斯
数值积分
代表(政治)
圆柱谐波
贝塞尔过程
类型(生物学)
拉盖尔多项式
区间(图论)
数学分析
应用数学
算法
物理
正交多项式
组合数学
经典正交多项式
生态学
Gegenbauer多项式
量子力学
政治
政治学
法学
生物
作者
Guidong Liu,Zhisheng Xu
标识
DOI:10.1016/j.rinam.2023.100429
摘要
This study focuses on the efficient and precise computation of Bessel transforms, defined as ∫abf(x)Jν(ωx)dx. Exploiting the integral representation of Jν(ωx), these Bessel transformations are reformulated into the oscillatory integrals of Fourier-type. When a>0, these Fourier-type integrals are transformed through distinct complex integration paths for cases with b<+∞ and b=+∞. Subsequently, we approximate these integrals using the generalized Gauss–Laguerre rule and provide error estimates. This approach is further extended to situations where a=0 by partitioning the integral’s interval into two separate subintervals. Several numerical experiments are provided to demonstrate the efficiency and accuracy of the proposed algorithms.
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