Given the Rodriguez formula P₁(x) = 2"n! dx" (x²-1)", show that Pm (x) = (1-x²)m/2 mm Pn(x) dm dam is a solution of the associated Legendre eqn. (1-x²)y" - 2xy' + [n(n + 1) — [m²]y = 0. Hint: show that the equation. can be obtained by differentiating the Legendre Equation (1-x²)z" - 2xz' + n(n+1)z = 0 m times w.r.t. x, followed by the substitution z = y(1-x²)-m/2.
Given the Rodriguez formula P₁(x) = 2"n! dx" (x²-1)", show that Pm (x) = (1-x²)m/2 mm Pn(x) dm dam is a solution of the associated Legendre eqn. (1-x²)y" - 2xy' + [n(n + 1) — [m²]y = 0. Hint: show that the equation. can be obtained by differentiating the Legendre Equation (1-x²)z" - 2xz' + n(n+1)z = 0 m times w.r.t. x, followed by the substitution z = y(1-x²)-m/2.
University Physics Volume 3
17th Edition
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:William Moebs, Jeff Sanny
Chapter7: Quantum Mechanics
Section: Chapter Questions
Problem 7.1CYU: Check Your Understanding If a=3+4i , what is the product a* a?
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OpenStax