【摘要】 <正>1引言Bessel函数是在物理和工程中应用较为广泛的一类函数,德国天文学家F.W.Bessel早在1824年就第一次提出了该函数.Bessel函数是Bessel微分方程x~2d~2y/dx~2+xdy/dx+(x~2-m~2)y=0,(1)的级数解,Bessel方程是在柱坐标或球坐标下使用分离变量法求解Laplace方程和Helmholtz方程时得到的，更多还原

【Abstract】 Gegenbauer’s addition theorem of Bessel function has been widely used in acoustic and electromagnetic scattering problems,especially in solving 3-D scattering problems by using fast multipole method.Based on the asymptotic bounds of Bessel and Neumann functions,this paper estimates the truncation error of Gegenbauer’s addition theorem,explicit bound and convergence order of the truncation error are obtained.The result is tested by some examples,which shows that the estimate is valid and sharp.更多还原