# Thread: legendre's polynomial...

1. ## legendre's polynomial...

ok i have a problem, that im having trouble getting started...

im supposed to use rodrigues formula, to find the Legendre's polynomials $P_{6}, P_{7} \and P_{8}.$

$\displaystyle P_{n}(x)=\frac{1}{2^{n}n!}\frac{d^{n}}{dx^{n}}(x^{ 2}-1)^{n}$ <---would I just plug into the equation for n=0,1,2,3,...

2. Originally Posted by slapmaxwell1
ok i have a problem, that im having trouble getting started...

im supposed to use rodrigues formula, to find the Legendre's polynomials $P_{6}, P_{7} \and P_{8}.$

$\displaystyle P_{n}(x)=\frac{1}{2^{n}n!}\frac{d^{n}}{dx^{n}}(x^{ 2}-1)^{n}$ <---would I just plug into the equation for n=0,1,2,3,...
The Rodriguez formula requires the computation of high order derivatives. An confortable alternative approach is the use of the recursive relation...

$\displaystyle \displaystyle P_{n+1} (x) = \frac{2n+1}{n+1}\ x\ P_{n} (x) - \frac{n}{n+1}\ P_{n-1} (x)$ (1)

... starting from $\displaystyle P_{0}(x)=1$ and $\displaystyle P_{1}(x)=x$...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$