To integrate a Legendre series, use the polynomial.legendre.legint() method in Python. The method returns the Legendre 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 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 an order of integration, must be positive. (Default: ... Read More

To generate a pseudo Vandermonde matrix of the Legendre polynomial, use the polynomial.legvander() method 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 Legendre 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 ... Read More

To generate a pseudo Vandermonde matrix of the Legendre polynomial, use the polynomial.legvander() method in Python NumpyThe 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 Legendre 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 Legendre series, use the polynomial.legendre.lagroots() method in Python. 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 parameter c is a 1-D array of coefficients.StepsAt first, import the required library −from numpy.polynomial import legendre as LCompute the roots of a Legendre series −j = complex(0, 1) print("Result...", L.legroots((-j, j)))Get the datatype −print("Type...", L.legroots((-j, j)).dtype)Get the shape −print("Shape...", L.legroots((-j, j)).shape)Examplefrom numpy.polynomial import legendre as L # To compute the roots of a Legendre series, use the ... Read More

To compute the roots of a Legendre series, use the polynomial.legendre.legroots() method in Python. 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 parameter c is a 1-D array of coefficients.StepsAt first, import the required library −from numpy.polynomial import legendre as LTo compute the roots of a Legendre series, use the polynomial.legendre.legroots() method in Python −print("Result...", L.legroots((0, 1, 2)))Get the datatype −print("Type...", L.legroots((0, 1, 2)).dtype)Get the shape −print("Shape...", L.legroots((0, 1, 2)).shape) Examplefrom numpy.polynomial import legendre as L # To compute the ... Read More

To generate a Legendre series, use the polynomial.legendre.legfromroots() method in Python. 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 legendre as LGenerate a Legendre series using the polynomial.legendre.legfromroots() method in Python −j = complex(0, 1) print("Result...", L.legfromroots((-j, j)))Get the datatype −print("Type...", L.legfromroots((-j, j)).dtype)Get the shape −print("Shape...", L.legfromroots((-j, j)).shape)Examplefrom numpy.polynomial import legendre ... Read More

To evaluate a Hermite_e series at points x, use the hermite.hermeval() method in Python Numpy. The 1st parameter, 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 coefficients ... Read More

To integrate a Legendre series, use the polynomial.legendre.legint() method in Python. The method returns the Legendre 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 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 an order of integration, must be positive. (Default: ... Read More

To generate a Vandermonde matrix of the Hermite_e polynomial, use the hermite_e.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 generate a Vandermonde matrix of the Hermite_e polynomial, use the hermite_e.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