classmethod Legendre.basis(deg, domain=None, window=None) [source] Series basis polynomial of degree deg. Returns the series representing the basis polynomial of degree deg. New in version 1.7.0. Parameters: deg : int Degree of the basis polynomial for the series. Must be >= 0. domain : {None, array_like}, optional If given, the array must be of the form [beg, end], where beg and end are the endpoints of the domain. If None is given then the class domain is used. The default is Non

Laguerre.__call__(arg) [source]

Laguerre.trim(tol=0) [source] 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. If all the coefficients would be removed the series is set to [0]. A new series instance is returned with the new coefficients. The current instance remains unchanged. Parameters: tol : non-negative number. All trailing coefficients less than tol will be removed. Returns: new_series : seri

Laguerre.truncate(size) [source] Truncate series to length size. Reduce the series to length size by discarding the high degree terms. The value of size must be a positive integer. This can be useful in least squares where the coefficients of the high degree terms may be very small. Parameters: size : positive int The series is reduced to length size by discarding the high degree terms. The value of size must be a positive integer. Returns: new_series : series New instance of series w

Laguerre.mapparms() [source] Return the mapping parameters. The returned values define a linear map off + scl*x that is applied to the input arguments before the series is evaluated. The map depends on the domain and window; if the current domain is equal to the window the resulting map is the identity. If the coefficients of the series instance are to be used by themselves outside this class, then the linear function must be substituted for the x in the standard representation of the base

Laguerre.roots() [source] Return the roots of the series polynomial. Compute the roots for the series. Note that the accuracy of the roots decrease the further outside the domain they lie. Returns: roots : ndarray Array containing the roots of the series.

Laguerre.linspace(n=100, domain=None) [source] Return x, y values at equally spaced points in domain. Returns the x, y values at n linearly spaced points across the domain. Here y is the value of the polynomial at the points x. By default the domain is the same as that of the series instance. This method is intended mostly as a plotting aid. New in version 1.5.0. Parameters: n : int, optional Number of point pairs to return. The default value is 100. domain : {None, array_like}, option

Laguerre.integ(m=1, k=[], lbnd=None) [source] Integrate. Return a series instance that is the definite integral of the current series. Parameters: m : non-negative int The number of integrations to perform. k : array_like Integration constants. The first constant is applied to the first integration, the second to the second, and so on. The list of values must less than or equal to m in length and any missing values are set to zero. lbnd : Scalar The lower bound of the definite integra

Laguerre.has_samewindow(other) [source] Check if windows match. New in version 1.6.0. Parameters: other : class instance The other class must have the window attribute. Returns: bool : boolean True if the windows are the same, False otherwise.

classmethod Laguerre.identity(domain=None, window=None) [source] Identity function. If p is the returned series, then p(x) == x for all values of x. Parameters: domain : {None, array_like}, optional If given, the array must be of the form [beg, end], where beg and end are the endpoints of the domain. If None is given then the class domain is used. The default is None. window : {None, array_like}, optional If given, the resulting array must be if the form [beg, end], where beg and end ar