Solutions in vicinit 例10.1 Legendre方程 U +(l+1)=0
Solutions in Vicinity of Regular Singularity Outlines & Conclusions) Example: Bessel Equation Solutions in Vicinity of Singularity Regular Singularity ~10.1 Legendre§ (1 − z 2 ) d 2w dz 2 − 2z dw dz + l(l + 1)w = 0 Xê´p(z) = − 2z 1 − z 2 q(z) = l(l + 1) 1 − z 2 z = ±1´p(z), q(z) 4: z = ±1Legendre§KÛ: C. S. Wu 1ù ~©§?ê){()
Solutions in vicinit 例10.1 Legendre方程 U +(l+1)=0 22 系数是p(2)= q(2) +1) 士1是(=)(2)的一阶极点 1为 Legen
Solutions in Vicinity of Regular Singularity Outlines & Conclusions) Example: Bessel Equation Solutions in Vicinity of Singularity Regular Singularity ~10.1 Legendre§ (1 − z 2 ) d 2w dz 2 − 2z dw dz + l(l + 1)w = 0 Xê´p(z) = − 2z 1 − z 2 q(z) = l(l + 1) 1 − z 2 z = ±1´p(z), q(z) 4: z = ±1Legendre§KÛ: C. S. Wu 1ù ~©§?ê){()
Solutions in vicinit 例10.1 Legendre方程 U +(l+1)=0 2z 系数是p(2) q(2) 2=1是p(2),q(2)的一阶极点 故2=士1为 Legendre方程的正则奇点
Solutions in Vicinity of Regular Singularity Outlines & Conclusions) Example: Bessel Equation Solutions in Vicinity of Singularity Regular Singularity ~10.1 Legendre§ (1 − z 2 ) d 2w dz 2 − 2z dw dz + l(l + 1)w = 0 Xê´p(z) = − 2z 1 − z 2 q(z) = l(l + 1) 1 − z 2 z = ±1´p(z), q(z) 4: z = ±1Legendre§KÛ: C. S. Wu 1ù ~©§?ê){()
Solutions in vicinit 例10.1 Legendre方程 U +(l+1)=0 1-2(3)(1+1) 2z 系数是p(2) z=±1是p(2),q(x)的一阶极点 故2=士1为 Legendre方程的正则奇点
Solutions in Vicinity of Regular Singularity Outlines & Conclusions) Example: Bessel Equation Solutions in Vicinity of Singularity Regular Singularity ~10.1 Legendre§ (1 − z 2 ) d 2w dz 2 − 2z dw dz + l(l + 1)w = 0 Xê´p(z) = − 2z 1 − z 2 q(z) = l(l + 1) 1 − z 2 z = ±1´p(z), q(z) 4: z = ±1Legendre§KÛ: C. S. Wu 1ù ~©§?ê){()
Solutions in vicinit 例10.2超几何( hypergeometric)方程 (1-2)d2+b-(1+a+)a2-aBm=0 尖
Solutions in Vicinity of Regular Singularity Outlines & Conclusions) Example: Bessel Equation Solutions in Vicinity of Singularity Regular Singularity ~10.2 AÛ(hypergeometric)§ z(1 − z) d 2w dz 2 + [γ − (1 + α + β)z] dw dz − αβw = 0 Xê´ p(z)= γ−(1+α+β)z z(1−z) q(z)=− αβ z(1−z) z = 0Úz = 1Ñ´p(z), q(z) 4: z = 0z = 1Ñ´AÛ§KÛ: C. S. Wu 1ù ~©§?ê){()