To remove small trailing coefficients from Legendre polynomial, use the legendre.legtrim() method in Python numpy. The method returns a 1-d array with trailing zeros removed. If the resulting series would be empty, a series containing a single zero is returned.The “Small” means “small in absolute value” and is controlled by the parameter tol; “trailing” means highest order coefficient(s), e.g., in [0, 1, 1, 0, 0] (which represents 0 + x + x**2 + 0*x**3 + 0*x**4) both the 3-rd and 4-th order coefficients would be “trimmed”. The parameter c is a 1-d array of coefficients, ordered from lowest order to ... Read More

To get the Least squares fit of Legendre series to data, use the legendre.legfit() method in Python numpy. The method returns the Legendre coefficients ordered from low to high. If y was 2-D, the coefficients for the data in column k of y are in column k.The parameter, x are the x-coordinates of the M sample (data) points (x[i], y[i]). The parameter, y are the y-coordinates of the sample points. Several sets of sample points sharing the same xcoordinates can be (independently) fit with one call to polyfit by passing in for y a 2-D array that contains one data ... Read More

To return the scaled companion matrix of a 1-D array of Legendre polynomial coefficients, use the legendre.legcompanion() method in Python Numpy. The usual companion matrix of the Legendre polynomials is already symmetric when c is a basis Laguerre polynomial, so no scaling is applied.Returns the scaled Companion matrix of dimensions (deg, deg). The parameter, c is a 1-D array of Legendre series coefficients ordered from low to high degree.StepsAt first, import the required library −import numpy as np from numpy.polynomial import legendre as LCreate a 1D array of coefficients −c = np.array([1, 2, 3, 4, 5])Display the array −print("Our Array...", ... Read More

To integrate a Hermite_e series, use the hermite_e.hermeint() method in Python. The 1st parameter, c is an array of Hermite_e series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.The 2nd parameter, m is an order of integration, must be positive. (Default: 1). The 3rd parameter, k is an integration constant(s). The value of the first integral at lbnd is the first value in the list, the value of the second integral at lbnd is the second value, etc. If k == [] (the default), all ... Read More

To integrate a Hermite_e series, use the hermite_e.hermeint() method in Python. The 1st parameter, c is an array of Hermite_e series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index. The 2nd parameter, m is an order of integration, must be positive. (Default: 1)The 3rd parameter, k is an integration constant(s). The value of the first integral at lbnd is the first value in the list, the value of the second integral at lbnd is the second value, etc. If k == [] (the default), all ... Read More

To evaluate a Legendre series at points x, use the polynomial.legendre.legval() method in Python Numpy. The 1st parameter is x. If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of c.The 2nd parameter, C, an array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the ... Read More

To differentiate a Hermite_e series, use the hermite_e.hermeder() method in Python. The 1st parameter, c is an array of Hermite_e series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.The 2nd parameter, m is the number of derivatives taken, must be non-negative. (Default: 1). The 3rd parameter, scl is a scalar. Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is for use in a linear change of variable. (Default: 1). The 4th parameter, axis is an Axis over which the ... Read More

To differentiate a Legendre series, use the polynomial.laguerre.legder() method in Python. Returns the Legendre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl.The 1st parameter, c is an array of Legendre series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index. The 2nd parameter, m is the number of derivatives taken, must be non-negative. (Default: 1). The 3rd parameter, scl is a scalar. Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is ... Read More

To differentiate a Legendre series, use the polynomial.laguerre.legder() method in Python. Returns the Legendre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl. The 1st parameter, c is an array of Legendre series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.The 2nd parameter, m is the number of derivatives taken, must be non-negative. (Default: 1). The 3rd parameter, scl is a scalar. Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is ... Read More

To evaluate a 2-D Hermite_e series on the Cartesian product of x and y, use the hermite.hermegrid2d(x, y, c) method in Python. The method returns the values of the two dimensional polynomial at points in the Cartesian product of x and y.The parameters are x, y. The two dimensional series is evaluated at the points in the Cartesian product of x and y. If x or y is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.The parameter, c is an ... Read More