# hypergeometric representation of Hermite $H_n(x)$

The DLMF has a hypergeometric representation for the Hermite polynomial $H_n(x)$ for real $x$, apparently.

$$H_n(x)=(2x)^n{}_2F_0\left(\frac{-\tfrac12n;-\tfrac12n+\tfrac12}{};-\frac{1}{x^2}\right)$$ (http://dlmf.nist.gov/18.5.E13)

This will give wrong results numerically with $n=333,x=1+i$ in Maxima and mpmath when compared with substitution into the polynomial. Is there such a representation for complex $z$? What would it be?

The motivation is to avoid substitution into the polynomial in the open source CAS Sage for precision reasons.

• This is an identity. mpmath gives the same value for the hypergeometric function and the polynomial with your values.
– juan
Mar 27, 2016 at 19:04
• I finally confirm. An error on my part. Many thanks. Can someone close the question please?
– rwst
Mar 27, 2016 at 19:54