What does $a$ mean in Taylor series formula? I'm trying to code the Taylor summation in MATLAB, being Taylor's formula the following:  

I've also seen $a$ denoted as $x_0$ in distinct bibliography.
Problem is that I'm not sure how should I evaluate or assign for $a$.
At lecture I studied the exponential Taylor's representation being: 
And I got to that same summation by evaluating $a$ as 0 but and I know that is meant to be McLaurin formula, but what's within evaluating with a different value or letting $a=x$?
What should I do in order to code properly Taylor summation for distinct functions?

$a$ is the point  for which you calculate the derivatives that you plug in the expansion, along with the displacement from $a$ raised to the correct power, as you seem to understand yourself
