The $\chi^2$ distribution PDF is $f_{\chi^2}(x;k) = \frac{1}{2^{k/2}\Gamma(k/2)} x^{k/2 - 1} \mathrm{e}^{-x/2} \mathbf{1}_{x \geq 0}$
I am trying to find a polynomial approximation to this density function. Power series expansion for the exponential $\mathrm{e}^x$ works fine, but it's an infinite series. I an looking at possibilities to attain a more compact approximation. Approximation using orthogonal polynomials is one option I'm looking at.
Are there better alternatives to power series expansion of $\mathrm{e}^x$ for approximating this pdf?