贝塞尔函数及贝塞尔三角函数矩的数值分析
Numerical analysis for the moments of Bessel functions and Bessel-trigonometric functions
AI总结：
本文基于贝塞尔函数的递推关系，研究了贝塞尔函数及贝塞尔三角函数矩的计算方法，提出高效方案近似一阶贝塞尔函数积分，并证明了贝塞尔三角函数矩的闭式表达。
摘要：
贝塞尔函数和贝塞尔三角函数的矩在许多实际问题和数值分析中起基本作用。本文基于贝塞尔函数的递推关系，对这些矩进行了完整分析。为数值计算贝塞尔函数的矩，提出了一种快速高效的方案来近似一阶贝塞尔函数的积分。证明了贝塞尔三角函数的矩可以表示为闭式。在数值结果中，首先验证了所提分析对贝塞尔函数矩的准确性和效率，然后通过与现有方法比较，提出了更优的贝塞尔函数矩计算方案。
英文摘要：
The moments of Bessel functions and Bessel-trigonometric functions play a basic role in many practical problems and numerical analysis. This paper presents a complete analysis for these moments based on the recursive relations of Bessel functions. To evaluate the moments of Bessel functions numerically, a fast and efficient scheme is also proposed to approximate the integral of Bessel function of the first kind and of zero order. The moments of Bessel-trigonometric functions are proved to be expressed in a closed form. In the numerical results, the accuracy and efficiency of the proposed analysis for the moments of Bessel functions is validated first and then by comparing the existing methods, a better scheme for the moments of Bessel functions is presented.
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