Connecting partial sums

Today’s exponential sum, like all the exponential sums on the site, is formed by drawing a line between consecutive partial sums of a series involving complex exponentials. The exponential sum page makes an image each day by putting the day’s month, day, and year into a formula.

Here’s today’s image

based on the sum

\sum_{n=0}^N \exp\left( 2\pi i \left( \frac{n}{8} + \frac{n^2}{19} + \frac{n^3}{25} \right ) \right )

I use American-style dates—month, day, year—because that increases the day-to-day variety of the images compared to using the day in the first denominator.

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