Chapter 6.4, Problem 21E

To determine

To verify: The result $I_v\left(x\right)=i^{-v}{J}_v\left(ix\right)$ is a real function, using the series $J_v\left(x\right)={\displaystyle \sum _{n=0}^{\infty }\frac{{\left(-1\right)}^n}{n!\Gamma \left(1+v+n\right)}{\left(\frac{x}{2}\right)}^{2n+v}}$.