Legendre and Bessel equations (intro)
General · Mathematics
Study notes
Q: Find P₂(x) (Legendre). What is J₀(0)? Rodrigues: P₂ = (1/2)(d²/dx²)(x²-1)² = (1/2)(12x²-4)/2... compute: (x²-1)² = x⁴-2x²+1. d²/dx²: 12x²-4. P₂ = (1/8)(12x²-4) = (3x²-1)/2! J₀(0): series Σ(-1)^k(x/2)^(2k)/(k!)²: at 0: 1! (P₂: quadrupole; J₀(0) = 1!)