%feature("docstring") OT::HermiteFactory
"Hermite specific orthonormal univariate polynomial family.

For the :class:`~openturns.Normal` distribution.

Available constructor:
    HermiteFactory()

Notes
-----
Any sequence of orthogonal polynomials has a recurrence formula relating any
three consecutive polynomials as follows:

.. math::

    P_{i + 1} = (a_i x + b_i) P_i + c_i P_{i - 1}, \quad 1 < i

The recurrence coefficients for the Hermite polynomials come analytically and
read:

.. math::

    \begin{array}{rcl}
        a_i & = & \displaystyle \frac{1}{\sqrt{i + 1}} \\
        b_i & = & 0 \\
        c_i & = & \displaystyle - \sqrt{\frac{i}{i + 1}}
    \end{array}, \quad 1 < i

See also
--------
StandardDistributionPolynomialFactory

Examples
--------
>>> import openturns as ot
>>> polynomial_factory = ot.HermiteFactory()
>>> for i in range(3):
...     print(polynomial_factory.build(i))
1
X
-0.707107 + 0.707107 * X^2"
