- #1

Demon117

- 165

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I am trying to work through and understand the derivation of the Legendre Polynomials from Jackson's Classical electrodynamics. I have reached a part that I cannot get through however. Jackson starts with the following orthogonality statement and jumps (as it seems) in his proof:

Equation 3.17 states:

[itex]\int P_{l'}[\frac{d}{dx} ([1-x^{2}]\frac{dP_{l}}{dx})+l(l+1)P_{l}(x)]dx=0[/itex]

He mentions integration by parts on the "first term" but I don't see how he gets to

Equation 3.18:

[itex]\int [(x^{2}-1)\frac{dP_{l}}{dx} \frac{dP_{l'}}{dx} +l(l+1)(P_{l'}(x)P_{l}(x))]dx=0[/itex]

I don't see this. Could someone please explain or give a hint to the intermediate step here? I'm afraid I just do not see it. Thanks.