To subtract one Legendre series from another, use the polynomial.legendre.legsub() method in Python Numpy. The method returns an array representing the Legendre series of their sum.Returns the difference of two Legendre series c1 - c2. The arguments are sequences of coefficients ordered 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 Legendre 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 Legendre series coefficients −c1 = ... Read More

To add one Legendre series to another, use the polynomial.legendre.legadd() method in Python Numpy. The method returns an array representing the Legendre series of their sum.Returns the sum of two Legendre series c1 + c2. The arguments are sequences of coefficients ordered 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 Legendre 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 Legendre series coefficients −c1 = ... Read More

To convert a polynomial to a Laguerre series, use the laguerre.poly2lag() method in Python Numpy. Convert an array representing the coefficients of a polynomial ordered from lowest degree to highest, to an array of the coefficients of the equivalent Laguerre series, ordered from lowest to highest degree.The method returns a 1-D array containing the coefficients of the equivalent Laguerre series. The parameter pol, is a 1-D array containing the polynomial coefficientsStepsAt first, import the required library −import numpy as np from numpy.polynomial import laguerre as LCreate an array using the numpy.array() method −c = np.array([1, 2, 3, 4, 5])Display the ... Read More

To convert a Laguerre series to a polynomial, use the laguerre.lag2poly() method in Python Numpy. Convert an array representing the coefficients of a Laguerre series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest to highest degree.The method returns a 1-D array containing the coefficients of the equivalent polynomial ordered from lowest order term to highest. The parameter c, is a 1-D array containing the Laguerre series coefficients, ordered from lowest order term to highest.StepsAt first, import the required library −import numpy as np from ... Read More

To remove small trailing coefficients from Laguerre polynomial, use the laguerre.lagtrim() 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 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 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 is 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 using ... Read More

To generate a Vandermonde matrix of the Hermite polynomial, use the chebyshev.hermvander() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where The last index is the degree of the corresponding Hermite polynomial. The dtype will be the same as the converted x.The parameter, x returns an Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array. The parameter, deg is the degree of the resulting ... 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 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