2026-04-28 21:46 UTC
Turning a trick into a technique
https://www.johndcook.com/blog/2026/04/28/even-series-trick/
Replies (1)
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@tpfto@mathstodon.xyz 2026-04-28 23:37
@johndcook@mathstodon.xyz the approximation you had derived in that post is also what you get when you try expanding the Bessel function into a series of cosines, using Bürmann's theorem (https://mathworld.wolfram.com/BuermannsTheorem.html) and then take the first two terms. \[ J_0(x)=1+\frac{\cos(x)-1}{2}-\frac{(\cos(x)-1)^2}{48}+\frac{7 (\cos(x)-1)^3}{1440}+\cdots\]