class numpy.polynomial.legendre.Legendre(coef, domain=None, window=None)[source]

A Legendre series class.

The Legendre class provides the standard Python numerical methods ‘+’, ‘-‘, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the attributes and methods listed in the ABCPolyBase documentation.


coef : array_like

Legendre coefficients in order of increasing degree, i.e., (1, 2, 3) gives 1*P_0(x) + 2*P_1(x) + 3*P_2(x).

domain : (2,) array_like, optional

Domain to use. The interval [domain[0], domain[1]] is mapped to the interval [window[0], window[1]] by shifting and scaling. The default value is [-1, 1].

window : (2,) array_like, optional

Window, see domain for its use. The default value is [-1, 1].

New in version 1.6.0.


basis(deg[, domain, window]) Series basis polynomial of degree deg.
cast(series[, domain, window]) Convert series to series of this class.
convert([domain, kind, window]) Convert series to a different kind and/or domain and/or window.
copy() Return a copy.
cutdeg(deg) Truncate series to the given degree.
degree() The degree of the series.
deriv([m]) Differentiate.
fit(x, y, deg[, domain, rcond, full, w, window]) Least squares fit to data.
fromroots(roots[, domain, window]) Return series instance that has the specified roots.
has_samecoef(other) Check if coefficients match.
has_samedomain(other) Check if domains match.
has_sametype(other) Check if types match.
has_samewindow(other) Check if windows match.
identity([domain, window]) Identity function.
integ([m, k, lbnd]) Integrate.
linspace([n, domain]) Return x, y values at equally spaced points in domain.
mapparms() Return the mapping parameters.
roots() Return the roots of the series polynomial.
trim([tol]) Remove trailing coefficients Remove trailing coefficients until a coefficient is reached whose absolute value greater than tol or the beginning of the series is reached.
truncate(size) Truncate series to length size.