User:Farley13/sandbox

2 comments on https://en.wikipedia.org/w/index.php?title=Bessel_function&action=history 1) The approximation seems incorrect - some minor tweaking provides a closer approximation - but even that seems like it could be quite a bit better:

J_{aprox}=\left(\frac{1}{6}+\frac{1}{3}\cos\left(\frac{x}{1.3}\right)+\frac{1}{3}\cos\left(\frac{\sqrt{3.9x}}{2.2}\right)+\frac{1}{6}\cos\left(x\right)\right)\cdot\frac{1}{1+\left(\frac{x}{7}\right)^{20}}+\sqrt{\frac{2}{\pi\cdot\operatorname{abs}\left(x\right)}}\cdot\cos\left(x-\frac{\pi}{4}\cdot\operatorname{sign}\left(x\right)\right)\cdot\left(1-\frac{1}{1+\left(\frac{x}{7}\right)^{20}}\right)

2) Might be good to mention that bessel's solution is basically frequency modulation where the carrier frequency is n