Why is $\sum{\frac{1}{(j/2)!}(\xi)^j}\approx\sum{\frac{1}{j!}(\xi)^{2j}}$?
This equation is used for solving the Schrödinger equation of the harmonic oscillator at one point in Griffiths, Introduction to Quantum Mechanics, chapter 2.3.2. He approximates the wave function (for great $\xi$) by $\psi(\xi)=h(\xi)e^{-\xi^{2}/2}$ and tries to find $h(\xi)$ using the power series $$h(\xi)=\sum_{j=0}^{\infty}a_j\xi^j$$ and later he says $$h(\xi)=C\sum{\frac{1}{(j/2)!}(\xi)^j}\approx C\sum{\frac{1}{j!}(\xi)^{2j}}\approx Ce^{\xi^2}$$ and this is the point that I do not understand.
Thanks for your help