言 Helmholtz方程在柱坐标系下分离变量,可得到 1d「df(r) r dr 5|F(7)=0 d7 若k2-A≠0,作变换r=Vk2-Ar,y(x)=R(r), 则方程变为(其中μ=v2 (v阶) Bessel方程 1d「dv/ r dx dz+ y(a) 本讲及下一讲集中讨论Bee方程的解及其性《尜 质,以及在分离变量法中的应用Bessel ftns & Neumann ftns Properties of Bessel ftns with Integer Order Fundamental Solutions to Bessel Equation Recurrence Relations Asymptotic Expansion Úó Helmholtz§3΋IXe©lCþ§Œ 1 r d dr  r dR(r) dr  + h k 2 − λ − µ r 2 i R(r) = 0 ek 2−λ6=0§ŠC†x= √ k 2−λr, y(x)=R(r)§ K§C(Ù¥µ = ν 2 ) (ν)Bessel§ 1 x d dx  x dy(x) dx  +  1 − ν 2 x 2  y(x) = 0 ù9eù8¥?ØBessel§)9Ù5 Ÿ§±93©lCþ{¥A^ C. S. Wu 1Êù μê()