Editing Legendre polynomials
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:<math>P_n (z) = \frac{1}{2 \pi i} \oint ( 1-2tz + t^2)^{1/2}~t^{-n-1} {\rm d}t</math> | :<math>P_n (z) = \frac{1}{2 \pi i} \oint ( 1-2tz + t^2)^{1/2}~t^{-n-1} {\rm d}t</math> | ||
Legendre polynomials can also be defined (Ref 1) using Rodrigues formula | '''Legendre polynomials''' can also be defined (Ref 1) using '''Rodrigues formula''' as: | ||
:<math> P_n(x) = \frac{1}{2^n n!} \frac{d^n}{dx^n} (x^2 - 1)^n </math> | :<math> P_n(x) = \frac{1}{2^n n!} \frac{d^n}{dx^n} (x^2 - 1)^n </math> | ||
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:<math>x^6= \frac{1}{231}[33P_0 (x) + 110P_2(x)+ 72P_4(x)+ 16P_6(x)]</math> | :<math>x^6= \frac{1}{231}[33P_0 (x) + 110P_2(x)+ 72P_4(x)+ 16P_6(x)]</math> | ||
==See also== | ==See also== | ||
*[[Associated Legendre function]] | *[[Associated Legendre function]] |