Series expansion with Legendre polynomials

I am trying to develop a code for the calculation of the electric potential outside of a spherical shell using series expansion and legendre polynomials.

where P_i(u) is the ith order legendre polynomial. Currently, I have this code:

 clear
 clc
 n = input('Enter number of iiterations (n): ' );
 x = .5;
 y = zeros(1,n);
 V = 2;
 for i = 1:n
     j(i) = ((legendreP(i+1,1)-legendreP(i-1,1))/(2*i+1))-(2*((legendreP(i+1,0)-legendreP(i-1,0))/(2*i+1)))+((legendreP(i+1,-1)-legendreP(i-1,-1))/(2*i+1));
     y(i) = ((2i+1)/2)*V*(j(i))*legendreP(i,x); 
 end
 print(y)

but I keep getting errors whenever I try to run it and I can't figure out why?

Any help would be appreciated

Answer 1

[David Goodmanson]

HI James,

I won't address how one might print the result, but the mistake in the algrbra is that you should use

y(i) = ((2*i+1)/2)*V*(j(i))*legendreP(i,x);
          ^

rather than

y(i) = ((2i+1)/2)*V*(j(i))*legendreP(i,x);

Personally I never use i, and not often j, for a for a loop index. It can get confused up with imaginary i or j, as in this case.

Answer 2

[Shraddha Kajle]

y(i) = ((2i+1)/2)*V*(j(i))*legendreP(i,x) and use y only at end instead of print(y)