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Line 2: In [[mathematics]] the '''Legendre rational functions''' are a sequence of functions which are both [[rational functions\|rational]] and [[orthogonal functions\|orthogonal]]. A rational Legendre function of degree ''n'' is defined as: :<math>R_n(x)~~\equiv~~ = \frac{\sqrt{2}}{x+1}\,L_n\left(\frac{x-1}{x+1}\right)</math> where <math>L_n(x)</math> is a [[Legendre polynomial]]. These functions are eigenfunctions of the singular Sturm-Liouville problem:

Legendre rational functions: Difference between revisions