Legendre rational functions: Difference between revisions

Revision as of 22:01, 20 August 2016

Revision as of 08:23, 3 August 2018

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A rational Legendre function of degree ''n'' is defined as:

:<math>R_n(x) = \frac{\sqrt{2}}{x+1}\,L_nP_n\left(\frac{x-1}{x+1}\right)</math>

where <math>L_nP_n(x)</math> is a Legendre polynomial. These functions are [[eigenfunction]]s of the singular [[Sturm-Liouville problem]]:

:<math>(x+1)\partial_x(x\partial_x((x+1)v(x)))+\lambda v(x)=0</math>