Translating Mathematical Formulas to Excel VBA

VBA's not really going to be your friend here. There isn't a built in integral function, but others have made one.

Then you could just set variables for e and T and z and pi, etc. like

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and use then that way in the equation.

However: the one thing I'm really not sure on is the infinity upper limit on your integration. No idea how to implement that. And I don't believe Excel natively supports calculus either, and though there appears to be ways to set it up, not sure how that would work with infinity.

There are basically two ways (whether in VBA or other programming language or with pencil/paper/sliderule) to evaluate integrals. You can use the Fundamental Theorem of Calculus where you come up with an antiderivative, evaluate at the upper and lower limit, and take the difference. Or you can use Riemann sum type algorithms https://en.wikipedia.org/wiki/Riemann_sum Walruseggman's link to MrExcel illustrates a Riemann sum type algorithm.

Assuming you use a Riemann sum to evaluate the integral, dealing with the upper limit of infinity simply means using a large enough number so that you know that the integral has "converged". If you have forgotten about "improper integrals", it would probably be worthwhile to review the calculus of improper integrals (top page from my internet search for convergence of improper integrals http://www.sosmath.com/calculus/impr...v/convdiv.html ). When considering computer round off error, you might also want to test whether it is important to perform the sum from low to high or from high to low or whether it does not matter.

At this point, it might be nice to know if you have a specific question related to implementing this in VBA or not. If it really is the "I have no idea where to start", then I think that these introduction to Riemann sums are probably as good a place to start as any. I might add that you might put some research into how others in your field have programmed this. If you can come across and antiderivative or similar formulation for this integral, it will likely simplify the programming quite a bit.