Difference between generating function and Rodrigue's formula?

[sreerajt]

What is the difference between generating function and Rodrigue's formula? Some says that from generating function you can generate required polynomial (say for example from generating function of Legendre polynomial you can get Legendre polynomial.), but in that case,as far as i know, Rodrigues formula also does the same job. So?

 

[maajdl]

see:
http://en.wikipedia.org/wiki/Generating_function
http://en.wikipedia.org/wiki/Rodrigues'_formula

 

[sreerajt]

i saw this link before posting this question. but i don't think that it contain answer to my question...

 

[vanhees71]

The generating function and the Rodrigues formula are just two ways to define the Legendre polynomials. Both have their merits in deriving formulas involving this set of orthogonal polynomials on the Hilbert space $\mathrm{L}^2([-1,1])$. Of course both definitions give the same polynomials.