The Special Function {H_{n}\left(x\right)}


1. Differential Equation[-]

The function {H_{n}\left(x\right)} satisfies the differential equation 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) }.

2. Derivative in Terms of Lower-Order Derivatives[+]

3. Expansion at 0[+]

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

The differential equation above has 0 non-zero finite singular pointsA complex numberĀ z_0 is a singular point (or singularity of a linear ordinary differential equation with polynomial coefficients, if the leading coefficient of the equation vanishes atĀ z_0..

4.1. Expansion at \infty [+]

5. Hypergeometric Representation[+]

6. Chebyshev Expansion over [-1,1][+]

7. Laplace Transform[+]

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 =