连带 Legendre方程在有界条件下的本征值问题 要求解本征值问题 d da (1 +|v(v+1) (+1)有界 必须先求解连带 Legendre方程
Associated Legendre Functions Spheroidal Harmonics Eigenproblem of Associated Legendre Eqns Orthogonality of Associated Legendre Ftns ëLegendre§3k.^e ¯K ¦) ¯K d dz 1 − z 2 dw dz + ν(ν + 1) − m2 1 − z 2 w = 0 w(±1)k. 7Lk¦)ëLegendre§ d dz 1 − z 2 dw dz + ν(ν + 1) − m2 1 − z 2 w = 0 {µ~©§?ê){ {µÏéÚLegendre§'X C. S. Wu 1lù ¥¼ê(n)
连带 Legendre方程在有界条件下的本征值问题 要求解本征值问题 d da (1 +|v(v+1) (+1)有界 必须先求解连带 Legendre方程 d+|v(v+1) 0
Associated Legendre Functions Spheroidal Harmonics Eigenproblem of Associated Legendre Eqns Orthogonality of Associated Legendre Ftns ëLegendre§3k.^e ¯K ¦) ¯K d dz 1 − z 2 dw dz + ν(ν + 1) − m2 1 − z 2 w = 0 w(±1)k. 7Lk¦)ëLegendre§ d dz 1 − z 2 dw dz + ν(ν + 1) − m2 1 − z 2 w = 0 {µ~©§?ê){ {µÏéÚLegendre§'X C. S. Wu 1lù ¥¼ê(n)
连带 Legendre方程在有界条件下的本征值问题 要求解本征值问题 d da (1 +|v(v+1) (+1)有界 必须先求解连带 Legendre方程 d+|v(v+1) 0 方法之一:常微分方程的幂级数解法 寻找和 Legendre方程的关系
Associated Legendre Functions Spheroidal Harmonics Eigenproblem of Associated Legendre Eqns Orthogonality of Associated Legendre Ftns ëLegendre§3k.^e ¯K ¦) ¯K d dz 1 − z 2 dw dz + ν(ν + 1) − m2 1 − z 2 w = 0 w(±1)k. 7Lk¦)ëLegendre§ d dz 1 − z 2 dw dz + ν(ν + 1) − m2 1 − z 2 w = 0 {µ~©§?ê){ {µÏéÚLegendre§'X C. S. Wu 1lù ¥¼ê(n)
连带 Legendre方程在有界条件下的本征值问题 要求解本征值问题 d da (1 +|v(v+1) (+1)有界 必须先求解连带 Legendre方程 d+|v(v+1) 0 方法之一:常微分方程的幂级数解法 方法之二:寻找和 Legendre方程的关系
Associated Legendre Functions Spheroidal Harmonics Eigenproblem of Associated Legendre Eqns Orthogonality of Associated Legendre Ftns ëLegendre§3k.^e ¯K ¦) ¯K d dz 1 − z 2 dw dz + ν(ν + 1) − m2 1 − z 2 w = 0 w(±1)k. 7Lk¦)ëLegendre§ d dz 1 − z 2 dw dz + ν(ν + 1) − m2 1 − z 2 w = 0 {µ~©§?ê){ {µÏéÚLegendre§'X C. S. Wu 1lù ¥¼ê(n)
连带 Legendre方程与 Legendre方程的关系 连带 Legendre方程 dd du d|+/(+1) 首先分析连带 Legendre方程在奇点处的性质 连带 Legendre方程的奇点和 Legendre方程完全 样,都是2=士1和 ,而且也都是正 则奇点
Associated Legendre Functions Spheroidal Harmonics Eigenproblem of Associated Legendre Eqns Orthogonality of Associated Legendre Ftns ëLegendre§Legendre§'X ëLegendre§ d dz 1 − z 2 dw dz + ν(ν + 1) − m2 1 − z 2 w = 0 Äk©ÛëLegendre§3Û:?5 ëLegendre§Û:ÚLegendre§ §Ñ´z = ±1Úz = ∞§ Ñ´ KÛ: 3z = ±1?I§´ ρ(ρ − 1) + ρ − m2 4 = 0 ¤±§Iρ = ±m/2 C. S. Wu 1lù ¥¼ê(n)