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To integrate a Hermite series, use the hermite.hermint() method in Python. This function integrates Hermite polynomials represented as coefficient arrays and allows you to set a custom lower bound for the integral. Syntax The syntax of hermite.hermint() is ? hermite.hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters The function accepts the following parameters ? Parameter Description Default c Array of Hermite series coefficients Required m Order of integration (must be positive) 1 k Integration constant(s) [] (zeros) lbnd Lower bound of the integral ... Read More
To evaluate a 3D Hermite series at points (x, y, z), use the hermite.hermval3d() method in NumPy. The method returns the values of the multidimensional polynomial on points formed with triples of corresponding values from x, y, and z. The first parameter consists of x, y, z coordinates. 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 ... Read More
To evaluate a 2D Hermite series at points (x, y), use the hermite.hermval2d() 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 first parameter contains x and y coordinates. 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. The second parameter, c, is an array of coefficients ordered so that the coefficient of the ... Read More
To evaluate a 3D Hermite series at points (x, y, z), use the hermite.hermval3d() 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. Syntax hermite.hermval3d(x, y, z, c) Parameters The function takes the following parameters ? x, y, z − The coordinates where the series is evaluated. Must have the same shape. Lists or tuples are converted to ndarrays c − Array of coefficients ordered so that the coefficient of term of multi-degree i, j, ... Read More
To evaluate a 3D Hermite series at points (x, y, z), use the hermite.hermval3d() method in NumPy. This method returns the values of the multidimensional polynomial on points formed with triples of corresponding values from x, y, and z coordinates. Syntax The basic syntax is − numpy.polynomial.hermite.hermval3d(x, y, z, c) Parameters The parameters are − 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 ... Read More
To integrate a Laguerre series and multiply by a scalar, use the numpy.polynomial.laguerre.lagint() method in Python. This method integrates the Laguerre series coefficients and applies a scaling factor before adding the integration constant. Syntax numpy.polynomial.laguerre.lagint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters The key parameters are ? c − Array of Laguerre series coefficients m − Order of integration (default: 1) k − Integration constant(s) (default: []) lbnd − Lower bound of integration (default: 0) scl − Scaling factor applied after each integration (default: 1) axis − Axis over which to integrate (default: ... Read More
To integrate a Laguerre series and set the lower bound of the integral, use the laguerre.lagint() method in Python. This method returns the Laguerre series coefficients integrated m times from the specified lower bound lbnd. At each iteration, the resulting series is multiplied by a scaling factor and an integration constant is added. Syntax numpy.polynomial.laguerre.lagint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters The key parameters for the lagint() method are ? c ? Array of Laguerre series coefficients m ? Order of integration (default: 1) k ? Integration constant(s) (default: []) lbnd ? ... Read More
To integrate a Hermite series, use the hermite.hermint() method in Python. This function integrates a Hermite polynomial series and allows you to specify the order of integration. Syntax numpy.polynomial.hermite.hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0) Parameters The function accepts the following parameters ? c ? Array of Hermite series coefficients. For multidimensional arrays, different axes correspond to different variables m ? Order of integration, must be positive (Default: 1) k ? Integration constant(s). If empty list (default), all constants are zero lbnd ? Lower bound of the integral (Default: 0) scl ? Scalar ... Read More
To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander2d() method in Python NumPy. The method returns a 2D pseudo-Vandermonde matrix where each element is evaluated using Laguerre polynomial basis functions at the given complex points. The method takes arrays of x and y coordinates and degree specifications to construct the matrix. The shape of the returned matrix is x.shape + (x_deg + 1) * (y_deg + 1), where the dtype matches the input arrays (complex128 for complex inputs). Syntax laguerre.lagvander2d(x, y, deg) Parameters The parameters are ? ... Read More
To differentiate a Hermite series, use the hermite.hermder() method in Python. This function allows you to compute derivatives of Hermite polynomial series with customizable scaling factors. Syntax numpy.polynomial.hermite.hermder(c, m=1, scl=1, axis=0) Parameters c − Array of Hermite series coefficients. If multidimensional, different axes correspond to different variables m − Number of derivatives taken, must be non-negative (Default: 1) scl − Scalar multiplier. Each differentiation is multiplied by scl, resulting in final multiplication by scl**m (Default: 1) axis − Axis over which the derivative is taken (Default: 0) Basic Differentiation Let's ... Read More