Laguerre Polynomials - Generalized Laguerre Polynomials

Generalized Laguerre Polynomials

For arbitrary real α the polynomial solution of the differential equation

x\,y'' + (\alpha +1 - x)\,y' + n\,y = 0

is called a generalized Laguerre polynomials, or associated Laguerre polynomials. The Rodrigues' formula for them are

L_n^{(\alpha)}(x)= {x^{-\alpha} e^x \over n!}{d^n \over dx^n} \left(e^{-x} x^{n+\alpha}\right).

The simple Laguerre polynomials are recovered from the generalized polynomials by setting α = 0:

Read more about this topic:  Laguerre Polynomials

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