The generalized Rodrigues formula is of the form(adsbygoogle = window.adsbygoogle || []).push({});

[tex]K_n\frac{1}{w}(\frac{d}{dx})^n(wp^n)[/tex]

The constant [itex]K_n[/itex] is seemingly chosen completely arbitrarily, & I really need to be able to figure out a quick way to derive whether it should be [itex]K_n = \tfrac{(-1)^n}{2^nn!}[/itex] in the case of Jacobi polynomials (reducable to Legendre, Chebyshev or Gegenbauer), [itex]K_n = \tfrac{1}{n!}[/itex] for Laguerre polynomials & [itex]K_n = (-1)^n[/itex] for Hermite polynomials. The best I have so far is actually working out the n'th derivative of [itex](wp^n)[/itex] in the case of Legendre polynomials, but that method becomes crazy with any of the other polynomials & as Hassani says the choices are arbitrary so they probably don't work. My question is, how do I get derive constants without any memorization, whether by some nice trick or by the method one uses to arbitrarily choose their values - I'd really appreciate it.

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# Normalization of Orthogonal Polynomials?

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