All of your functions look similar to the example function which I showed. It should not be too difficult to use my example as a model for the rest of the functions.

Your functions look simple enough that you might be able to write all of this in Excel and avoid the usually much more difficult problem of getting two programs to cooperate with each other and pass data back and forth.

There is the product Excel Link which allows you to use the power of Mathematica from within Excel without having to manually operate two programs.

Just as a very small example to try to introduce you to Mathematica, this uses Mathematica by itself to calculate Za[Xa]

Clear[vstar, m]; 
ber[x_] := Sum[(-1)^n*(x/2)^(4 n)/((2 n)!)^2, {n, 0, m-1}];
bei[x_] := Sum[(-1)^(n-1)*(x/2)^(4 n-2)/((2 n-1)!)^2, {n, 1, m}];
berprime[x_] := Sum[(-1)^(n-1)*(2 n)*(x/2)^(4 n-1)/((2 n)!)^2, {n, 1, m}]; 
beiprime[x_] := Sum[(-1)^(n-1)*(2 n-1)*(x/2)^(4 n-3)/((2 n-1)!)^2, {n, 1, m}];
psi1[x_] := bei[x]+(1-vstar)/x*berprime[x]; 
psi2[x_] := ber[x]+(1-vstar)/x*beiprime[x]; 
Za[Xa_] := beiprime[Xa]*psi2[Xa]-berprime[Xa]*psi1[Xa];

Then

m = 3;
vstar = 5.5;
Xa = 7.2;
Za[Xa]

returns a value of

-368.605

There is more that Mathematica could do, but perhaps this simple example can give you an idea how to define your other functions and verify that all the results are correct. After that you might be able to look at further automation of the process.