Category:Definitions/Laguerre Polynomials

This category contains definitions related to Laguerre Polynomials.
Related results can be found in Category:Laguerre Polynomials.

The Laguerre polynomials are the solutions to Laguerre's differential equation:

$x \dfrac {\d^2 y} {\d x^2} + \paren {1 - x} \dfrac {\d y} {\d x} + \alpha y = 0$

for $\alpha = n$.

They are of the form:

$\map {L_n} x = e^x \map {\dfrac {\d^n} {\d x^n} } {x^n e^{-x} }$