MHB How is Rodrigue's Formula Derived?

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how do we derive rodrigue's formula
 

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dansingh said:
how do we derive rodrigue's formula

Hi dansingh,

Welcome to MHB! The method of deriving this is given at this link;

Legendre polynomials and Rodrigues' formula

Let us know if you have any further questions with the derivation. :)
 
n(x)=(x2-1)n. (20)

By differentiation we see that it satisfies the following first order differential equation,
(1-x2)f'n+2nxfn=0.
how did you get itb pleasez explain me the differentiation part
 

Thread 'A question about variables of integration'

I have the equation ##F^x=m\frac {d}{dt}(\gamma v^x)##, where ##\gamma## is the Lorentz factor, and ##x## is a superscript, not an exponent. In my textbook the solution is given as ##\frac {F^x}{m}t=\frac {v^x}{\sqrt {1-v^{x^2}/c^2}}##. What bothers me is, when I separate the variables I get ##\frac {F^x}{m}dt=d(\gamma v^x)##. Can I simply consider ##d(\gamma v^x)## the variable of integration without any further considerations? Can I simply make the substitution ##\gamma v^x = u## and then...
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