2
$\begingroup$

I am looking for references that discuss solutions of the equation

$\tan x=-a x$

(for $x,a\in \mathbb{R}$). I know about the graphical approaches, and any number of numerical solution approaches, but I was wondering if there's a semi-closed form solution, which gives something like

$x = f(a,c)$

where $c$ is a (set of) numerically solved constants which are independent of $a$ (i.e. a set of constants corresponding to the set of roots).

I've come up with an approach (i.e. a function $f$), but I figure this has been solved already, so I'd prefer to reference that ``known'' solution.

  • 0
    $x=0$ for $a=0$. For $a=-1$, you have the small-angle approximation (Wikipedia: Small-angle approximation: https://en.wikipedia.org/wiki/Small-angle_approximation)2017-10-28

0 Answers 0