Associated Legendre functions P k n (x) are needed, e g , in quantum physics They are defined by and are solutions of the ODE where q(x) n(n 1) k 2 (1 x 2 ) Find P 1 1 (x), P 1 2 (x), P 2 2 (x), and P 2 4 (x) and verify that they satisfy (16) P(x) (1 x) x 2 d Pn(x) dxk (1 x)y 2xy q(x)y 0...

P11x 123x2 1 P12x 321 x2 P22x 325x3 3x P24x 1521 x232 Verification For ...

Associated Legendre functions P k n (x) ? are needed, e.g., in quantum physics. They are defined

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Associated Legendre functions P^k_n(x)_?are needed, e.g., in quantum physics. They are defined by

and are solutions of the ODE

where q(x) = n(n + 1) - k²/(1 - x²). Find P¹₁(x), P¹₂(x), P²₂(x), and P²₄(x) and verify that they satisfy (16).

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Advanced Engineering Mathematics

ISBN: 978-0470458365

10th edition

Authors: Erwin Kreyszig

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Associated Legendre functions P k n (x) ? are needed, e.g., in quantum physics. They are defined

Question:

P(x) = (1 - x²) x/2 d Pn(x) – dxk (1-x²)y" - 2xy + q(x)y = 0

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Advanced Engineering Mathematics

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