Question13) (Bessel Function) The domain of Bessel function $J_{3}(x)=\sum_{k=0}^{\infty}(-1)^{k} \frac{x^{2 k+3}}{2^{2 k+1} k!(k+3)!}$ is A) $(-1,1)$ B) $(-\infty, \infty)$ C) $(0,1)$ D) $(-1,0)$

Studdy Solution
Conclude the domain based on the ratio test result.
Since the limit of the ratio is 0 for all $x$, the series converges for all $x \in (-\infty, \infty)$.
Therefore, the domain of the Bessel function $J_3(x)$ is $(- \infty, \infty)$, which corresponds to option B.
Solution: The domain of $J_3(x)$ is $\boxed{B}$.