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# scipy.special.eval_hermite

scipy.special.eval_hermite(n, x, out=None) = <ufunc 'eval_hermite'>

  Evaluate physicist’s Hermite polynomial at a point.

  Defined by

  \[H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2};\]

  \(H_n\) is a polynomial of degree \(n\). See 22.11.7 in [AS] or [DLMF] for details.

  Parameters:
    n array_like

      Degree of the polynomial

    x array_like

      Points at which to evaluate the Hermite polynomial

    out ndarray, optional

      Optional output array for the function values

  Returns:
    H scalar or ndarray

      Values of the Hermite polynomial

  See also

  `roots_hermite`

    roots and quadrature weights of physicist’s Hermite polynomials

  `hermite`

    physicist’s Hermite polynomial object

  `numpy.polynomial.hermite.Hermite`

    Physicist’s Hermite series

  `eval_hermitenorm`

    evaluate Probabilist’s Hermite polynomials

  References

  [AS]

  Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.

  [DLMF]

  NIST Digital Library of Mathematical Functions, https://dlmf.nist.gov/18.5.T1