关键词: 贝塞尔函数, Prony-like方法, 三角函数, 基于傅里叶级数展开, 数值逼近

Abstract: Numerical approximations of Bessel functions are both of important theoretical significance and widely applied in mathematics, physics, engineering. In this work, we apply two variants of Prony's method on Bessel functions of the first kind of integer order. The Prony-like methods in cosine or sine version yield approximations as sums of sinusoidal functions of Bessel functions of the first kind of integer order. In the symbolic computation software Maple, we compute the approximations for different orders and over different intervals, and compare these approximations with those obtained through the Fourier method. Experiments show that Prony-like methods perform much better than the Fourier method.

Key words: Bessel functions, Prony-like methods, trigonometric functions, Fourierbased method, numerical approximation