1y01dx2dx2RrYxx
球贝塞尔方程
在柱坐标系中：
1u12u2uuzzRZ2kV022z
02AcosmBsi
m2m012m0ZCDz0ZCezDezzz00ZCcoshzDsi
hzh22d2RdRxx2m2R0xk2x2dxdx


综上所述，对于齐次的波动方程、输运方程、稳定场方程在球、柱坐标系中有如下解的形式：①u0
1lurAcosmBsi
mCrDrl1m012221x2d2xdll1m0xcosdx2dx1x2
uzAcosmBsi
mZzRm01210ZCDzREmFme2dRdRZCeuzDeuzx22xx2m2R0xu0dxdxd2RdR0ZCcosmzDsi
mzx22xx2m2R0xudxdx
utta23u0②uta23u0uVtT3Vk2V0TtCcoskatDsi
katTtCek
22
at
3Vk2V0
fVrAcosmBsi
mRrm0122dm22dll11x22x0xcosdxdx1x2d2ydy1x22xx2ly0xkrYxxRrdxdx2


VzAcosmBsi
mZzRm012zCDz0zCeuzDeuzZZ000zCcoshzDsi
hzd2RdRx22xx2m2R0xk2dxdx


§41常点邻域的级数解法用球坐标和柱坐标对齐次波动、输运、稳定场方程进行r