Note: I am using 2*x+cos(x)
as an example below. I'm asking this question for any function where Solve[]
doesn't yield a closed form result. My specific interest at the moment is getting Mathematica to spit out the (well known) power series expansion solution of Kepler's Equation of the Center, just as a test.
The function 2*x+cos(x)
is monotonic increasing (derivative is 2-sin(x)
), and thus invertible. There's no simple form for the inverse:
Solve[2*x+Cos[x] == y, x]
Solve::nsmet: This system cannot be solved with the methods available to Solve.
Question: can I get a power series approximation to the solution? Either using Mathematica builtin functions or some sort of voodoo?
Cos[x]
as a power series and solving the polynomial, but that doesn't really give me a power series. $\endgroup$