F = ztrans(f) is the Z-transform of the scalar f with default independent variable n.  If f is not a function of n, then f is  assumed to be a function of the independent variable returned by findsym(f,1). The default return is a function of z.

If f = f(z), then ztrans returns a function of w.

By definition,  where the summation above proceeds with respect to z.

ztrans(f,w) makes f a function of the variable w instead of the default z.

ztrans(f,k,w) takes f to be a function of k instead of the default n. The summation is then with respect to w.

The ztrans(M) function computes the element-wise Z-transform of M.  The result, R, is formed as R[i,j] = ztrans(M[i,j], n,z).