# Bessel function

1. Sep 15, 2008

### Harmony

Last edited by a moderator: May 3, 2017
2. Sep 17, 2008

### gabbagabbahey

Since $$y' (x)$$ contains only odd powers of x, the n=1 term does not vanish when you take the derivative of the series. Therefore,

$$y'' (x)= \sum_{n=1}^{\infty} \frac{(-1)^n (2n)(2n-1) x^{2n-2}}{4^n (n!)^2}$$

The extra $$x/2$$ in your answer will be canceled by the $$n=1$$ term.