Daily Archives: December 3, 2020

Sideband #70: The exp Function


Back in October I published two posts involving the ubiquitous exponential function. [see: Circular Math and Fourier Geometry] The posts were primarily about Fourier transforms, but the exponential function is a key aspect of how they work.

We write it as ex or as exp(x) — those are equivalent forms. The latter has a formal definition that allows for the complex numbers necessary in physics. That definition is of a series that converges on an answer of increasing accuracy.

As a sidebar, I thought I’d illustrate that convergence. There’s an interesting non-linear aspect to it.

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