# 1. Differential Equation[-]

The function $${H_{n}\left(x\right)}$$ satisfies the differential equation$$\displaystyle {\frac {d^{2}}{d{x}^{2}}}y \left( x \right) -2\,x{\frac {d}{dx}}y \left( x \right) +2\,ny \left( x \right) = 0$$ with initial values $$y \left( 0 \right) =\frac{{2}^{n}\sqrt {\pi }}{\Gamma \left( 1/2-1/2\,n \right) }$$ and $$y' \left( 0 \right) =-\frac{{2}^{n+1}\sqrt {\pi }}{\Gamma \left( -1/2\,n \right) }$$.

# 4. Local Expansions at Singularities and at Infinity[-]

The differential equation above has 0 non-zero finite .

# 8. Parameters[-]

The Hermite function $${H_{n}\left(x\right)}$$ depends on the parameter $$n$$. The box below can be used to rename or instantiate this parameter.
p1 =