5
votes
1answer
77 views

How to find inverse of $\sin(x) + \sin(2x) = y$?

I was wondering if there were any way to solve the equation $$\sin(x) + \sin(2x) = y$$ in terms of $x$. This of course would allow us to express the inverse for this function on $-\frac{\pi}{4}$ to ...
4
votes
2answers
196 views

Taylor series of the inverse of $x^4+x$

I would like to expand the inverse function of $$g(x) := x^4+x $$ in a taylor series at the point x = 0. I calculated the first and second derivate at x = 0 with the rule of the derivation of an ...
1
vote
0answers
55 views

Looking for examples where $f(z)=\operatorname{inv} \int_{0}^{z} g(z)\, dz$ with $f(z)$ entire and $g(z)$ not meromorphic.

I'm looking for examples where $f(z)=\operatorname{inv}\int_{0}^{z} g(z) \, dz$ with $f(z)$ entire and $g(z)$ not meromorphic. For clarity, by $\operatorname{inv}$, I mean the functional inverse. ...
0
votes
2answers
152 views

Domain of convergence of $f^{-1}: \mathbb R ^N \mapsto \mathbb R^N$ taylor series

In another question, I ask about the topology of the singular manifold of the Jacobian. What i want to ask in here is about the radius of convergence of a Taylor series expansion of the inverse ...