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{{Short description|Sequence of orthogonal functions on [0, ∞)}}
[[Image:LegendreRational1.png|thumb|300px|Plot of the Legendre rational functions for n=0,1,2 and 3 for ''x'' between 0.01 and 100.]]
In [[mathematics]], the '''Legendre rational functions''' are a sequence of [[orthogonal functions]] on [0, ∞). They are obtained by composing the [[Cayley transform]] with [[Legendre polynomials]].
A rational Legendre function of degree ''n'' is defined as:
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