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

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

To generate a pseudo Vandermonde matrix of the Legendre polynomial with x, y, z sample points, use the legendre.legvander3d() method in Python Numpy. Returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y, z).The parameters, x, y ,z are arrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. The parameter, deg is a list of maximum degrees of the form [x_deg, y_deg, z_deg].StepsAt first, import the required library −import numpy as np from ... Read More

To generate a pseudo Vandermonde matrix of the Legendre polynomial with x, y, z sample points, use the legendre.legvander3d() method in Python Numpy. Returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y, z).The parameters, x, y ,z are arrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. The parameter, deg is a list of maximum degrees of the form [x_deg, y_deg, z_deg].StepsAt first, import the required library −import numpy as np from ... Read More

To evaluate a 3D Hermite_e series at points (x, y, z), use the hermite.hermeval3d() method in Python Numpy. The method returns the values of the multidimensional polynomial on points formed with triples of corresponding values from x, y, and z.The 1st parameter is x, y, z. The three dimensional series is evaluated at the points (x, y, z), where x, y, and z must have the same shape. If any of x, y, or z 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 ... Read More

To evaluate a 2D Hermite_e series at points (x, y), use the hermite.hermeval2d() method in Python Numpy. The method returns the values of the two dimensional polynomial at points formed with pairs of corresponding values from x and y.The 1st parameter is x, y. The two dimensional series is evaluated at the points (x, y), where x and y must have the same shape. 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 2nd parameter, C, ... Read More

To divide one Hermite_e series by another, use the polynomial.hermite.hermediv() method in Python Numpy. The method returns an array of Hermite_e series coefficients representing the quotient and remainder.Returns the quotient-with-remainder of two Hermite_e series c1 / c2. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters, c1 and c2 are 1-D arrays of Hermite_e series coefficients ordered from low to high.StepsAt first, import the required library −import numpy as np from numpy.polynomial import hermite as HCreate 1-D arrays of Hermite_e series coefficients −c1 ... Read More

To multiply one Hermite_e series to another, use the polynomial.hermite.hermemul() method in Python Numpy. The method returns an array representing the Hermite_e series of their product. Returns the product of two Hermite_e series c1 * c2. The arguments are sequences of coefficients, from lowest order “term” to highest, e.g., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters 1-D arrays of Hermite_e series coefficients ordered from low to high.StepsAt first, import the required library −import numpy as np from numpy.polynomial import hermite_e as HCreate 1-D arrays of Hermite_e series coefficients −c1 = np.array([1, 2, 3]) c2 ... Read More