To evaluate a 3-D polynomial at points (x, y, z), use the polynomial.polyval3d() 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. The parameters are x, y, z. The three dimensional series is ... Read More

To generate a pseudo Vandermonde matrix of the Chebyshev polynomial, use the chebyshev.chebvander() in Python Numpy. The method returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y). The parameter x, y are the arrays of point coordinates, all of the same shape. The dtypes will be converted ... Read More

To evaluate a polynomial specified by its roots at points x, use the polynomial.polyvalfromroots() 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 ... Read More

To generate a monic polynomial with given roots, use the polynomial.polyfromroots() method in Python Numpy. The method returns the 1-D array of the polynomial’s coefficients If all the roots are real, then out is also real, otherwise it is complex. The parameter roots are the sequence containing the roots.StepsAt first, ... Read More

To Integrate a polynomial, use the polynomial.polyint() method in Python. Returns the polynomial 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 ... Read More

To generate a pseudo Vandermonde matrix of the Chebyshev polynomial, use the chebyshev.chebvander() in Python Numpy. The method returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y).The parameter x, y are the arrays of point coordinates, all of the same shape. The dtypes will be converted to ... Read More

To generate a Vandermonde matrix of the Chebyshev polynomial, use the chebyshev.chebvander() in Python Numpy. The method returns the Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where The last index is the degree of the corresponding Chebyshev polynomial. The dtype will be ... Read More

To generate a Vandermonde matrix of the Chebyshev polynomial, use the chebyshev.chebvander() in Python Numpy. The method returns the Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where The last index is the degree of the corresponding Chebyshev polynomial. The dtype will be ... Read More

The arctanh is a multivalued function: for each x there are infinitely many numbers z such that tanh(z) = x. The convention is to return the z whose imaginary part lies in [-pi/2, pi/2]. The inverse hyperbolic tangent is also known as atanh or tanh^-1.To compute the inverse Hyperbolic tangent ... Read More

To calculate the n-th discrete difference, use the numpy.diff() method. The first difference is given by out[i] = a[i+1] - a[i] along the given axis, higher differences are calculated by using diff recursively. The diff() method returns the n-th differences. The shape of the output is the same as a ... Read More