/usr/include/openturns/swig/OrthogonalUniVariatePolynomial_doc.i is in libopenturns-dev 1.7-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 | %feature("docstring") OT::OrthogonalUniVariatePolynomial
"Base class for orthogonal univariate polynomials.
.. warning::
Orthogonal univariate polynomials are not intended to be created manually.
They should be constructed with the subclasses of
:class:`~openturns.OrthogonalUniVariatePolynomialFamily` (like e.g.
:class:`~openturns.HermiteFactory`). Constructor parameters are therefore
intentionally not documented.
See Also
--------
OrthogonalUniVariatePolynomialFamily
Examples
--------
>>> import openturns as ot
Create a univariate polynomial from a list of coefficients:
>>> for i in range(3):
... print(ot.OrthogonalUniVariatePolynomialFamily().build(i))
1
X
-0.707107 + 0.707107 * X^2"
// ---------------------------------------------------------------------
%feature("docstring") OT::OrthogonalUniVariatePolynomial::getRecurrenceCoefficients
"Accessor to the recurrence coefficients.
Returns
-------
recurrence_coefficients : list of :class:`NumericalPoint`
The list of recurrence coefficients that defined the orthogonal univariate
polynomial from the very first univariate orthogonal polynomial
:math:`P_0`.
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 i > 1
Examples
--------
>>> import openturns as ot
>>> polynomial = ot.OrthogonalUniVariatePolynomialFamily().build(2)
>>> print(polynomial.getRecurrenceCoefficients())
[[1,0,0],[0.707107,0,-0.707107]]"
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