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This is a very simple question. Why is Rademacher's formula presented with d/dx in it?

The partition formula.

Why not just "do" the derivative? enter image description here

Then replace x with n?

Is it so there is only one transcendental function in the formula? Or am I totally mis-reading this thing. I am slowly making my way through the original paper, but I wanted to just plug something in to it (calculate p(5)...for example) to see how it worked.

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AFAICT it just makes the formula look a little less forbidding, and also this is the representation of the function that comes out naturally through the proof of the formula (at least in some of its derivations). I don't think you should be reading too much into that.

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