Are you specifically looking at a binomial expansion? If so, there's a trick for composing that.
For a generalized "raise this number to this value and multiply by this coefficient", you can still use arrays, and take advantage of elementwise operators. In general, elementwise operators are what will enable you to use arrays in a function handle.
For your example above:
p1 = [2,1,1];
c1 = [1,2,1];
x1 = [1,2,3];
f=@(x,p,c) sum(c.*(x.^p));
f(x1,p1,c1)
8
In my experience, the utility of anonymous functions is best for small functions without much logic, or as handlers for binding specific values to more generalized functions. If you need a loop or specialty access logic, it's often simpler in the long run to create a dedicated function.
A related tool for arrays in functions is arrayfun, which applies a function to all entries in an array.
arrayfun(@(x) x+2, x1)
[3, 4, 5]
It can take multiple inputs as well, allowing us to replicate the above in a slightly different way:
sum (arrayfun(@(x,p,c) c*x^p, x1,p1,c1))
8
