基于李群方法的贝塞尔函数数学实现

Mathematical derivation of Bessel functions from Lie group theory

基于李群的表示理论,首先讨论了欧拉群的表示及其性质;然后,从该群的表示理论出发,分别导出了第一类贝塞尔函数的积分形式和幂级数形式.该研究表明了群方法可以求解对称边界问题的解析波函数,并为用群方法求解电磁场问题创造了条件.

This paper is from a Lie-group theoretical background, firstly the representation and properties of Euclidean group are discussed; Afterwards integral and power series representations of Bessel functions of the first kind are derived from the representation of Euclidean group. The study shows that analytic wave functions of symmetry boundary condition can be obtained in group approach, which creates conditions forsolving electromagnetic problems by group method.