chaospy.expansion.chebyshev_1

chaospy.expansion.chebyshev_1(order, lower=- 1, upper=1, physicist=False, normed=False, retall=False)

Chebyshev polynomials of the first kind.

Args:

order (int):

The polynomial order.

lower (float):

Lower bound for the integration interval.

upper (float):

Upper bound for the integration interval.

physicist (bool):

Use physicist weights instead of probabilist.

Returns:

(numpoly.ndpoly, numpy.ndarray):

Chebyshev polynomial expansion. Norms of the orthogonal expansion on the form E(orth**2, dist).

Examples:

>>> polynomials, norms = chaospy.expansion.chebyshev_1(4, retall=True)
>>> polynomials
polynomial([1.0, q0, q0**2-0.5, q0**3-0.75*q0, q0**4-q0**2+0.125])
>>> norms
array([1.       , 0.5      , 0.125    , 0.03125  , 0.0078125])
>>> chaospy.expansion.chebyshev_1(3, physicist=True)
polynomial([1.0, q0, 2.0*q0**2-1.0, 4.0*q0**3-2.5*q0])
>>> chaospy.expansion.chebyshev_1(3, lower=0.5, upper=1.5, normed=True).round(3)
polynomial([1.0, 2.828*q0-2.828, 11.314*q0**2-22.627*q0+9.899,
            45.255*q0**3-135.765*q0**2+127.279*q0-36.77])