Editing Hermite polynomials (section)

===Hypergeometric functions===
The physicist's Hermite polynomials can be expressed as a special case of the [[parabolic cylinder function]]s:
<math display="block">H_n(x) = 2^n U\left(-\tfrac12 n, \tfrac12, x^2\right)</math>
in the [[right half-plane]], where {{math|''U''(''a'', ''b'', ''z'')}} is [[confluent hypergeometric function|Tricomi's confluent hypergeometric function]]. Similarly,
<math display="block">\begin{align}
 H_{2n}(x) &= (-1)^n \frac{(2n)!}{n!} \,_1F_1\big(-n, \tfrac12; x^2\big), \\
 H_{2n+1}(x) &= (-1)^n \frac{(2n+1)!}{n!}\,2x \,_1F_1\big(-n, \tfrac32; x^2\big),
\end{align}</math>
where {{math|<sub>1</sub>''F''<sub>1</sub>(''a'', ''b''; ''z'') {{=}} ''M''(''a'', ''b''; ''z'')}} is [[confluent hypergeometric function|Kummer's confluent hypergeometric function]].

There is also<ref>[https://dlmf.nist.gov/18.5#E13 DLMF Equation 18.5.13]</ref><math display="block">H_{n}\left(x\right)=(2x)^{n}{{}_{2}F_{0}}\left({-\tfrac{1}{2}n,-\tfrac{1}{2}n+\tfrac{1}{2}\atop-};-\frac{1}{x^{2}}\right).</math>