Interpolation trilogy

This weekend I wrote three blog posts related to polynomial interpolation.

First, I looked into a claim I found in a book saying that by using quadratic interpolation rather than linear interpolation, you could reduce a 541 pages of sine function values to just one page. The claimed turns out to be a mistake, though you can achieve substantial compression by using higher order interpolation.

Next, I looked at Bessel’s formula and Everett’s formula for interpolation. You’ll hardly ever see these formulas mention in contemporary math books, but you’ll see them a lot in older books. Why’s that?

Finally, the coefficients in Bessel’s and Everett’s formulas are examples of binomial coefficients with non-integer arguments. The middle post was deliberately high-level, not explicitly giving the coefficients. The last post gives the coefficients explicitly because they are examples of generalized binomial coefficients. As I say in that post “These more general binomial coefficients are in this liminal zone of topics that come up regularly, but not so regularly that they’re widely known.”