How I can code this Nonuniform Series?

Hi all,

I have a problem in coding of series below:

from n=0 & P0(x)=1. I used handle function in a for loop but I couldn't to save the handle function at the end of each iteration. I appreciate you if you could help me on this problem.

Thanks

[Kevin Chng]

Do you mind post your for loop function with your handle function?

[Dimitris Kalogiros]

Two questions:

1) What is the definition of Pn(x) ?

2) Do you have "symbolic math toolbox" license ?

[Torsten]

Do these recursively defined polynomials have a name ?

Then maybe googling this name together with "matlab" will give you hints on how to efficiently calculate them.

[mohamad hoseini]

This is gram-schmidt orthogonalization or process. I have the symbolic math toolbox on my MATLAB. I'll post my code below despite dear "Dimitris Kalogiros" posted a perfect answer to my question.

Answer 1

[Dimitris Kalogiros]

Provided that you can use symbolic math toolbox, I suggest the following:

close all; clc; clearvars;

syms n x Pn(x) 

% first N polynomials
N=5;
f{N}=0;

% definition for n=0
Pn(x)=1;
f{1}=Pn(x);

% calculation from n=1 up to n=N 
for n=1:N

      Pn(x)=x^n;
      for k=1:n
          Pn(x)=Pn(x)- ( int((x^n)*f{k},x,-1,1) / int(f{k}^2,x,-1,1)  )* f{k} ; 
      end

      %store next polynomial 
      f{n+1}=Pn(x);

end

%display all calculated polynomials
for k=0:N
    fprintf(' for n = %d    ', k);
    disp(f{k+1})
end

If you run it , lets say , to calculate P1(x), P2(x),...,P5(x) , you'll get something like this:

The "tip" here is to use the cell array f{}, in order to store all Pn(x) polynomials.

[Walter Roberson]

Alternatively you could phrase it as P{n+1}(x). Which is to say that you can use a cell array of function handles to solve the coding, without using symbolic toolbox.

This is a situation where I would want to analyze to see whether memoize() is appropriate.

[mohamad hoseini]

That works completely right dear Dimitris. I appreciate you for sharing your knowledge on my question. I was not familiar with this toolbox before and I know something valuable now.