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)