MATLAB: Can’t get the Maclaurin Series function to use symsum properly

derivativemaclaurin seriestrigonometric series

Here is the code I'm working with currently:
function [ output_args ] = MaclaurinSeries( f,a,tol )
syms x k;
y = subs(f,a)
disp(f)
i=1
error = 1;
while error > tol
    f1 = symsum(diff(f,x,k) * (x^k)/(factorial(k)),k,0,i)
    error = y - subs(f1,a)
    q = subs(f1,a)
    i=i+1
end
Every time I run it, no matter how many times I tweak it, I manage to get f1 = 0 every time (which just isn't true). It calculates the derivative properly and everything, but I just don't know why it's returning zero. Any help?

Best Answer

symsum(diff(f,x,k) * (x^k)/(factorial(k)),k,0,i)
is processed as
temp = diff(f,x,k) * (x^k)/(factorial(k));
symsum(temp, k, 0, i)
That is, the expression is evaluated first (as is the case for all MATLAB function arguments) and the result of the expression has the symsum applied to it.
But diff(f, x, k) with symbolic k is 0 . I do not know why they made that choice.
With it coming out as 0, you are doing symsum(0, k, 0, i) which is going to be 0.
I would advise not using symsum for this. Instead, keep a running total, adding one more term at each point.
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