To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander() 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 Laguerre 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 ... Read More

To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander() 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 Laguerre 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 ... Read More

To Compute the roots of a Laguerre series, use the laguerre.lagroots() method in Python Numpy. The method returns an array of the roots of the series. If all the roots are real, then out is also real, otherwise it is complex.The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively insensitive to ... Read More

To Compute the roots of a Laguerre series, use the laguerre.lagroots() method in Python Numpy. The method returns an array of the roots of the series. If all the roots are real, then out is also real, otherwise it is complex.The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively insensitive to ... Read More

To generate a Laguerre series with given roots, use the laguerre.lagfromroots() method in Python Numpy. The method is 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 −from numpy.polynomial import laguerre as LTo generate a Laguerre series with given roots, use the laguerre.lagfromroots() method −j = complex(0, 1) print("Result...", L.lagfromroots((-j, j)))Get the datatype −print("Type...", L.lagfromroots((-j, j)).dtype)Get the shape ... Read More

To generate a Laguerre series with given roots, use the laguerre.lagfromroots() 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 −from numpy.polynomial import laguerre as LTo generate a Laguerre series with given roots, use the laguerre.lagfromroots() method in Python Numpy −print("Result...", L.lagfromroots((-1, 0, 1)))Get the datatype −print("Type...", L.lagfromroots((-1, 0, 1)).dtype)Get the ... Read More

To integrate a Laguerre series, use the laguerre.lagint() method in Python. The method returns the Laguerre 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 scaling factor is for use in a linear change of variable.The 1st parameter, c is an array of Laguerre 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: ... Read More

To differentiate a Laguerre series, use the laguerre.lagder() method in Python. The method returns the Laguerre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl. The argument c is an array of coefficients from low to high degree along each axis, e.g., [1, 2, 3] represents the series 1*L_0 + 2*L_1 + 3*L_2 while [[1, 2], [1, 2]] represents 1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y) if axis=0 is x and axis=1 is y.The 1st parameter, c is an array of Laguerre series coefficients. If c is multidimensional the different axis correspond ... Read More

To differentiate a Laguerre series, use the laguerre.lagder() method in Python. The method returns the Laguerre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl. The argument c is an array of coefficients from low to high degree along each axis, e.g., [1, 2, 3] represents the series 1*L_0 + 2*L_1 + 3*L_2 while [[1, 2], [1, 2]] represents 1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y) if axis=0 is x and axis=1 is y.The 1st parameter, c is an array of Laguerre series coefficients. If c is multidimensional the different axis correspond ... Read More

To differentiate a Laguerre series, use the laguerre.lagder() method in Python. The method returns the Laguerre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl. The argument c is an array of coefficients from low to high degree along each axis, e.g., [1, 2, 3] represents the series 1*L_0 + 2*L_1 + 3*L_2 while [[1, 2], [1, 2]] represents 1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y) if axis=0 is x and axis=1 is y.The 1st parameter, c is an array of Laguerre series coefficients. If c is multidimensional the different axis correspond ... Read More