# Partition function vs config integral

by aaaa202
Tags: config, function, integral, partition
 P: 185 Maybe this will be a little more clear. The Riemann definition of the integral is something like this: $$\int_0^\infty f(x) dx = \lim_{\Delta x \rightarrow 0} \sum_{n = 0}^{\infty} f(n \Delta x) \Delta x$$ Rewriting $$\frac{1}{\Delta x}\int_0^\infty f(x) dx = \lim_{\Delta x \rightarrow 0} \sum_{n = 0}^{\infty} f(n \Delta x)$$ You can make this into an appoximation by dropping the limit: $$\frac{1}{\Delta x}\int_0^\infty f(x) dx \approx \sum_{n = 0}^{\infty} f(n \Delta x)$$ This is often done the other way; the computation of an integral numerically on a computer is approximation as a summation.