On power series representing solutions of the one-dimensional time-independent Schrödinger equation

For the equation $\chi''(x)=u(x)\chi(x)$ with infinitely smooth $u(x)$, the general solution $\chi(x)$ is found in the form of a power series. The coefficients of the series are expressed via all derivatives $u^{(m)}(y)$ of the function $u(x)$ at a fixed point $y$. Examples of solutions for particular functions $u(x)$ are considered.