关于 Legendre方程的讨论 Legendre方程 dd du d2/+u=0 ★还可以在z=1(或z=-1)点的邻域内求 解 Legendre方程
Legendre Polynomials Properties of Legendre Polynomials Solutions to the Legendre Equation Legendre Polynomials 'uLegendre§?Ø Legendre§ d dz 1 − z 2 dw dz + λw = 0 F ±3z = 1(½z = −1):S¦ )Legendre§ C. S. Wu 18ù ¥¼ê()
关于 Legendre方程的讨论 Legendre方程 dd du d2/+u=0 ★z=±1是方程的正则奇点,方程在环 域0<|z-11<2内有两个正则解
Legendre Polynomials Properties of Legendre Polynomials Solutions to the Legendre Equation Legendre Polynomials 'uLegendre§?Ø Legendre§ d dz 1 − z 2 dw dz + λw = 0 F z = ±1´§KÛ:§§3 0 < |z − 1| < 2SküK) C. S. Wu 18ù ¥¼ê()
关于 Legendre方程的讨论 Legendre方程 dd du d2/+u=0 ★z=±1是方程的正则奇点,方程在环 域0<|z-11<2内有两个正则解 ★故可设 ()=(x-1)∑cn(2-1)
Legendre Polynomials Properties of Legendre Polynomials Solutions to the Legendre Equation Legendre Polynomials 'uLegendre§?Ø Legendre§ d dz 1 − z 2 dw dz + λw = 0 F z = ±1´§KÛ:§§3 0 < |z − 1| < 2SküK) F w(z) = (z − 1)ρX ∞ n=0 cn(z − 1)n C. S. Wu 18ù ¥¼ê()
关于 Legendre方程的讨论 Legendre方程 d du +入=0 d ★代入 legendre方程,就可以得到在z=1点的 指标方程 p(p-1)+p=0=p1=P2=0
Legendre Polynomials Properties of Legendre Polynomials Solutions to the Legendre Equation Legendre Polynomials 'uLegendre§?Ø Legendre§ d dz 1 − z 2 dw dz + λw = 0 F \Legendre§§Ò±3z = 1: I§ ρ(ρ − 1) + ρ = 0 =⇒ ρ1 = ρ2 = 0 C. S. Wu 18ù ¥¼ê()
关于 Legendre方程的讨论 Legendre方程 d du +入=0 d ★代入 legendre方程,就可以得到在z=1点的 指标方程 p(p-1)+p=0=p1=P2=0 ★说明 Legendre方程在z=1点邻域内的第一解 在圆域2-1<2解析,而第二解则一定含类 有对数项,以z=1(和之=-1)为枝点
Legendre Polynomials Properties of Legendre Polynomials Solutions to the Legendre Equation Legendre Polynomials 'uLegendre§?Ø Legendre§ d dz 1 − z 2 dw dz + λw = 0 F \Legendre§§Ò±3z = 1: I§ ρ(ρ − 1) + ρ = 0 =⇒ ρ1 = ρ2 = 0 F `²Legendre§3z = 1:S1) 3 |z − 1| < 2)Û§ 1)K½¹ ké꧱z = 1(Úz = −1){: C. S. Wu 18ù ¥¼ê()