I am reading Jackson's electrodynamics book. When I went through the Legendre polynomial, I have a question.(adsbygoogle = window.adsbygoogle || []).push({});

In the book, it stated that from the Rodrigues' formula we have

Consider only the odd terms

[itex]\int_0^1dx\;P_l(x)=\left(-\frac{1}{2}\right)^{\frac{l-1}{2}}\frac{(l-2)!!}{2\left(\frac{l+1}{2}\right)!}[/itex]How to obtain this equation and how can I obtain the equation for even terms?

Thanks in advance.

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# Legendre Polynomial and Rodrigues' Formula

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