can functions in matlab be related to other functions within the same mfile?

I'm trying to set up a general mfile to calculate a required function when given a selected data point and a group of known x values and f(x) values using Newton's interpolation of polynomials of orders 1 through 3.

As per the equations for solving this, there are a lot of functions within other functions. Can matlab read and calculate these?

for example:

you have:

x1 = 2.5 x2 = 3 x3 = 4 x4 = 5

and the related f(x) values are:

f(x1) = 6.5 f(x2) = 7 f(x3) = 3 f(x4) = 1

and you want to interpolate for:

f(x)

when x = 3.4

in between x2 and x3 above

setting x = 3.4 (given value to solve) as:

a = 3.4

to change the variable x allowing it to be used below

the first set of equations are as follows, which relate to x and f(x) values:

Eq.1) f(x2,x1) = ((f(x2)-f(x1))/(x2-x1))

Eq.2) f(x3,x2) = ((f(x3)-f(x2))/(x3-x2))

Eq.3) f(x4,x3) = ((f(x4)-f(x3))/(x4-x3))

For the second set of equations, I need to relate to Eq.1 (f(x2,x1), Eq.2 (f(x3,x2) and Eq.3 f(x4,x3).

Is it possible for me to write this for the second set of equations:

Eq.4) f(x3,x2,x1) = ((f(x3,x2)-f(x2,x1))/(x3-x1))

Eq.5) f(x4,x3,x2) = ((f(x4,x3)-f(x3,x2))/(x4-x2))

and the third set of equations, relating to the second set of equations (Eq.4 and Eq.5) as:

Eq.6) f(x4,x3,x2,x1) = ((f(x4,x3,x2)-f(x3,x2,x1))/(x4-x1))

Using Eq's 1 through 6, I can then solve for the desired order as follows (f1 being order 1, f2 being order 2 and f3 being order 3):

f1(a) = f(x1)+f(x2,x1)*(a-x1)

f2(a) = f1(a)+f(x3,x2,x1)*(a-x1)*(a-x2)

f3(a) = f2(a)+f(x4,x3,x2,x1)*(a-x1)*(a-x2)*(a-x3)

The whole purpose of this is to link all the equations together so that only the first4 x values and first 4 f(x) values need to be changed and the system will then interpolate the required info solving for f(a).

Is this possible? I have tried several different ways of creating this mfile however matlab doesn't seem to want to link the f(x1,x2) etc. together..

How can this be done?