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To raise a Chebyshev series to a power, use the chebyshev.chebpow() method in Python Numpy. Returns the Chebyshev series c raised to the power pow. The argument c is a sequence of coefficients ordered from low to high. i.e., [1, 2, 3] is the series T_0 + 2*T_1 + 3*T_2. The method returns the Chebyshev series of power.The parameter, c is a 1-D array of Chebyshev series coefficients ordered from low to high. The parameter, power is a power to which the series will be raised. The parameter, maxpower is the maximum power allowed. This is mainly to limit growth ... Read More
To divide one Chebyshev series by another, use the polynomial.chebyshev.chebdiv() method in Python Numpy. The method returns arrays of Chebyshev series coefficients representing the quotient and remainder.Returns the quotient-with-remainder of two Chebyshev series c1 / c2. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1, 2, 3] represents the series T_0 + 2*T_1 + 3*T_2. The parameters c1 and c2 are 1-D arrays of Chebyshev series coefficients ordered from low to high.StepsAt first, import the required libraries -import numpy as np from numpy.polynomial import chebyshev as CCreate 1-D arrays of Chebyshev series coefficients −c1 = ... 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 multiply one Chebyshev series to another, use the polynomial.chebyshev.chebmul() method in Python. The method returns an array of Chebyshev series coefficients representing their product. Returns the product of two Chebyshev series c1 * c2. The arguments are sequences of coefficients, from lowest order “term” to highest, e.g., [1, 2, 3] represents the series T_0 + 2*T_1 + 3*T_2. The parameters c1 and c2 are 1-D arrays of Chebyshev series coefficients ordered from low to high.StepsAt first, import the required libraries -import numpy as np from numpy.polynomial import chebyshev as CCreate 1-D arrays of Chebyshev series coefficients −c1 = np.array([1, ... Read More
To raise a Hermite_e series to a power, use the polynomial.hermite.hermepow() method in Python Numpy. The method returns Hermite_e series of power. Returns the Hermite_e series c raised to the power pow. The argument c is a sequence of coefficients ordered from low to high. i.e., [1, 2, 3] is the series P_0 + 2*P_1 + 3*P_2. The parameter, c is a 1-D array of Hermite_e series coefficients ordered from low to high.The parameter, pow is a Power to which the series will be raised. The parameter, maxpower is the maximum power allowed. This is mainly to limit growth of ... Read More
To evaluate a Legendre series at multi-dimensional array of points x, use the polynomial.legendre.legval() method in Python Numpy. The 1st parameter is 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 ... Read More
To differentiate a Legendre series, use the polynomial.laguerre.legder() method in Python. Returns the Legendre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl. 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 the number of derivatives taken, must be non-negative. (Default: 1). The 3rd parameter, scl is a scalar. Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is ... Read More
To differentiate a Legendre series, use the polynomial.laguerre.legder() method in Python. Returns the Legendre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by sclThe 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 the number of derivatives taken, must be non-negative. (Default: 1). The 3rd parameter, scl is a scalar. Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is ... Read More
To evaluate a 2D Hermite_e series at points (x, y), use the hermite.hermeval2d() 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 1st parameter is x, y. 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, otherwise it is left unchanged and if it isn’t an ndarray it is treated as a scalar.The 2nd parameter, C, ... Read More
To evaluate a 2D Hermite_e series at points (x, y), use the hermite.hermeval2d() 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 1st parameter is x, y. 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, otherwise it is left unchanged and if it isn’t an ndarray it is treated as a scalar.The 2nd parameter, C, ... Read More