[sf.cmath.hermite]

🔗

floating-point-type hermite(unsigned n, floating-point-type x);
float        hermitef(unsigned n, float x);
long double  hermitel(unsigned n, long double x);

Effects: These functions compute the Hermite polynomials of their respective arguments n and x.

Returns:

{H n (x), where {H n is given by Formula 29.36, n is n, and x is x .}_{n is given by Formula 29.36, n is n, and x is x .}}_{n (x), where {H n is given by Formula 29.36, n is n, and x is x .}_{n is given by Formula 29.36, n is n, and x is x .}}

\begin{matrix} {H n (x) = (- 1 {) n {e {x 2 {d n d {x n}^{n}}^{n d {x n}^{n}}}^{2 {d n d {x n}^{n}}^{n d {x n}^{n}}}}^{{x 2 {d n d {x n}^{n}}^{n d {x n}^{n}}}^{2 {d n d {x n}^{n}}^{n d {x n}^{n}}}}}^{n {e {x 2 {d n d {x n}^{n}}^{n d {x n}^{n}}}^{2 {d n d {x n}^{n}}^{n d {x n}^{n}}}}^{{x 2 {d n d {x n}^{n}}^{n d {x n}^{n}}}^{2 {d n d {x n}^{n}}^{n d {x n}^{n}}}}}}_{n (x) = (- 1 {) n {e {x 2 {d n d {x n}^{n}}^{n d {x n}^{n}}}^{2 {d n d {x n}^{n}}^{n d {x n}^{n}}}}^{{x 2 {d n d {x n}^{n}}^{n d {x n}^{n}}}^{2 {d n d {x n}^{n}}^{n d {x n}^{n}}}}}^{n {e {x 2 {d n d {x n}^{n}}^{n d {x n}^{n}}}^{2 {d n d {x n}^{n}}^{n d {x n}^{n}}}}^{{x 2 {d n d {x n}^{n}}^{n d {x n}^{n}}}^{2 {d n d {x n}^{n}}^{n d {x n}^{n}}}}}} \end{matrix}

Remarks: The effect of calling each of these functions is implementation-defined if n >= 128.

29 Numerics library [numerics]

29.7 Mathematical functions for floating-point types [c.math]

29.7.6 Mathematical special functions [sf.cmath]

29.7.6.16 Hermite polynomials [sf.cmath.hermite]