To multiply a Laguerre series by an independent variable, use the polynomial.laguerre.lagmulx() method in Python. Multiply the Laguerre series c by x, where x is the independent variable. The parameter c is a 1-D array of Laguerre series coefficients ordered from low to high.StepsAt first, import the required library −import numpy as np from numpy.polynomial import laguerre as LCreate an array −c = np.array([1, 2, 3])Display the array −print("Our Array...", c)Check the Dimensions −print("Dimensions of our Array...", c.ndim)Get the Datatype −print("Datatype of our Array object...", c.dtype)Get the Shape −print("Shape of our Array object...", c.shape)To multiply a Laguerre series by an ... Read More

To subtract one Laguerre series from another, use the polynomial.laguerre.lagsub() method in Python Numpy. The method returns an array of Laguerre series coefficients representing their difference. Returns the difference of two Laguerre series c1 - c2. The sequences of coefficients are from lowest order term to highest, i.e., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters c1 and c2 are 1-D arrays of Laguerre series coefficients ordered from low to high.StepsAt first, import the required library −import numpy as np from numpy.polynomial import laguerre as LCreate 1-D arrays of Laguerre series coefficients −c1 = np.array([1, ... Read More

To generate a pseudo Vandermonde matrix of the Hermite polynomial and x, y, z sample points, use the hermite.hermvander3d() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The parameter, 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 the list of maximum degrees of the form [x_deg, y_deg, z_deg].StepsAt first, import the required library −import numpy as np from numpy.polynomial import hermite as HCreate arrays of ... Read More

To generate a pseudo Vandermonde matrix of the Hermite polynomial, use the hermite.hermvander2d() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The parameter, x, y are an array 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 the list of maximum degrees of the form [x_deg, y_deg].StepsAt first, import the required library −import numpy as np from numpy.polynomial import hermite as HCreate arrays of point coordinates, all of the same shape ... Read More

To generate a Hermite series with given roots, use the hermite.hermfromroots() method in Python Numpy. The method returns a 1-D array of coefficients. If all roots are real then out is a real array, if some of the roots are complex, then out is complex even if all the coefficients in the result are real. The parameter roots are the sequence containing the roots.StepsAt first, import the required library −import numpy as np from numpy.polynomial import hermite as HTo generate a Hermite series with given roots, use the hermite.hermfromroots() method in Python Numpy −print("Result...", H.hermfromroots((-1, 0, 1)))Get the datatype −print("Type...", ... Read More

To Integrate a Chebyshev series, use the chebyshev.chebint() method in Python. Returns the Chebyshev series coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is added. The 1st parameter, c is an array of Chebyshev 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 ... Read More

To Integrate a Chebyshev series, use the chebyshev.chebint() method in Python. Returns the Chebyshev series coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is added. The 1st parameter, c is an array of Chebyshev 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 ... Read More

To Integrate a Chebyshev series, use the chebyshev.chebint() method in Python. Returns the Chebyshev series coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is added. The 1st parameter, c is an array of Chebyshev 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 ... Read More

To integrate a Hermite series, use the hermite.hermint() method in Python. The 1st parameter, c is an array of Hermite 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 2-D Laguerre series on the Cartesian product of x and y, use the polynomial.laguerre.laggrid2d() method in Python. The method returns the values of the two dimensional Laguerre series at points in the Cartesian product of x and y.If c has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape + y.shape. The 1st parameter, x, y is the two dimensional series is evaluated at the points in the Cartesian product of x and y. If x or y is a list ... Read More