Talk:Legendre rational functions

[Untitled]

There is a problem on the page because if

$R_{0}(x)=1\,$

$R_{1}(x)={\frac {x-1}{x+1}}\,$

$R_{2}(x)={\frac {x^{2}-4x+1}{(x+1)^{2}}}\,$

$R_{3}(x)={\frac {x^{3}-9x^{2}+9x-1}{(x+1)^{3}}}\,$

$R_{4}(x)={\frac {x^{4}-16x^{3}+36x^{2}-16x+1}{(x+1)^{4}}}\,$

then

$\lim _{x\rightarrow \infty }(x+1)R_{n}(x)={\sqrt {2}}$

could not be... i think there s some sort of mixup with the polynoms...

Indeed, there is a confusion about the modified Legendre rational functions and the Legendre rational functions. The latter has no 1/(x+1), just the sqrt(2) normalization. By the way, some authors cite the formula without the sqrt(2)...

A cleanup is required to make the possible definitions of functions clearly separated.

References: LRF: Guo,Shen,Wang: J Sci Comput (15), 117 mod LRF: Guo, Shen: Indiana Univ J of Math 50(2001) 181

An application: Parand, Razzaghi: Physica Scripta, 69 (2004) 353

Szabolcs —Preceding unsigned comment added by Mazsx (talk • contribs) 15:17, 31 January 2008 (UTC)