legendre polynomial and terms

hello,i have to solve this type of legendre polynomial: Pk+2(x) = ((2*k+3)/(k+2))*x*Pk+1(x) - ((k+1)/(k+2))* Pk(x), plus i want to find the root of P6(x) (6 digits accuracy) . I am a begginer so your help is significant! Thank you!

[John BG]

have you realised that the first part of your question is the same as the recursion formula shown in MATLAB help for the MATLAB function.

Replace in your expression k+2=n

legendrep(n,x)

.

.

in same MATLAB help you can read how to find roots of these polynomials:

roots = vpasolve(legendreP(6,x) == 0)
roots =
 -0.93246951420315202781230155449399
 -0.66120938646626451366139959501991
 -0.23861918608319690863050172168071
  0.23861918608319690863050172168071
  0.66120938646626451366139959501991
  0.93246951420315202781230155449399

[bk97]

thanks a lot my friend i appreciate your hep. I just had a probem with the toolbox and i avoided to use this comand.Now it's fixed. But tell me , what is the command for 6 digits accuracy of this root?

[Walter Roberson]

vpa(roots,6)