%feature("docstring") OT::HistogramPolynomialFactory
"Histogram specific orthonormal univariate polynomial family.

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

Available constructor:
    HistogramPolynomialFactory(*first, width, height*)

Parameters
----------
first : float
    Lower bound.
width : positive sequence of float
    :math:`\ell_i` is the width of the class :math:`i`.
height : positive sequence of float
    :math:`h_i` is the frequency of the class :math:`i`.

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 HistogramPolynomial polynomials are computed from the recurrence of the associated monic polynomials (see :class:`~openturns.AdaptiveStieltjesAlgorithm`) but with an exact evaluation of the dot-products.

See also
--------
StandardDistributionPolynomialFactory

Examples
--------
>>> import openturns as ot
>>> polynomial_factory = ot.HistogramPolynomialFactory(1.0, [1.0, 2.0], [4.0, 2.0])
>>> for i in range(3):
...     print(polynomial_factory.build(i))
1
-2.56273 + 1.13899 * X
7.80593 - 7.42767 * X + 1.5268 * X^2
"
