i have a recurrence function L(x). I have L1(x), L2(x).... L4(x) as can you see on the image followed. how can I write a matlab program to generate it's different polynoms till L50(x) for example.

|monospac

 twoed|

[Torsten]

You forgot to include the recurrence relation.

Best wishes

Torsten.

[constantin chanou]

the recurrence relation is:

Answer 1

[Titus Edelhofer]

Hi Constantin,

polynomials are "encoded" as vectors of the coefficients. So you would have (shifting the index by 1):

L{1} = 1;
L{2} = [-1 1];
L{3} = [0.5 -2 1];

If you have the recurrence relation, as Torsten mentioned, you can create the loop (and use e.g. conv to "multiply" polynomials).

Titus

[constantin chanou]

Thanks Titus but I succeeded to generate it till L(4). My main concern was how to create a loop using conv. the recurrence relation is:

[Titus Edelhofer]

Shouldn't be too difficult anymore:

• Rearrange to have L_n on one side of the equation
• x+2n-1 would be [1 2*n-1]
• Loop over n to "compute" L{n}

Titus

[Titus Edelhofer]

Although I'm not sure if you did everything right so far. Either the recursion is wrong or L2 is wrong (or I am wrong) ...

Titus

[Torsten]

I guess the OP means Laguerre polynomials:

n*L_n(x)+(x-2*n+1)*L_(n-1)(x)+(n-1)*L_(n-2)(x)=0

Best wishes

Torsten.

[Titus Edelhofer]

Another hint: the polynomials in the recurrence need to have the same order, so you will need to add

[0 0 (n-1)*L{(n-2)+1}]

Titus