Questions tagged [lagrange-inversion]

I am writing a piece of research where I use the Lagrange inversion formula for solving some equation. More precisely, for $y=f(x)$ where $f$ is analytic at $x=a$ and such that $f'(a)\neq 0$, we have \begin{equation} x = a + \sum_{n\ge…

I have to show that $$\frac{2}{1+(1+x)^{1/2}} = 1 - \frac{k}1\cdot\frac{x}4 + \frac{k(k+3)}{2!}\cdot\left(\frac{x}4\right)^2-\frac{k(k+4)(k+5)}{3!}\cdot\left(\frac{x}4\right)^3+\ldots$$ I need to start with $z = a + \frac{x}z$ to find the Lagrange…