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# Class Chebyshev2

source code

Chebyshev polynomials of the second kind, orthonormal over (-1, 1) with weight (1-x^2)^(1/2). Called Un(x) in Abramowitz and Stegun.

Instance Methods

 __init__(self, n=None, x=None) Argument n is how many points you want the polynomials evaluated at. source code

 recurse(self, n, fn, fnm1) Does the recurrence relation, evaluating f_(n+1) as a function of n, f_n, and f_(n-1). source code

 wt_(self) source code

 P(self, i) Self.P(i) is the ith orthogonal polynomial. (Inherited from gmisclib.ortho_poly.ortho_poly) source code

 compute(self, n) (Inherited from gmisclib.ortho_poly.ortho_poly) source code

 expand(self, c) (Inherited from gmisclib.ortho_poly.ortho) source code

 wt(self) Weighting function to get orthonormality. (Inherited from gmisclib.ortho_poly.ortho) source code

 x_(self, m) Calculates the points at which the function is evaluated, if you want m evenly spaced points. (Inherited from gmisclib.ortho_poly.ortho) source code
 Class Variables __doc__ = `"""Chebyshev polynomials of the second ki...` name = `'Chebyshev2'` registry = `{}` (Inherited from gmisclib.ortho_poly.ortho)
 Method Details

### __init__(self, n=None, x=None)(Constructor)

source code

Argument n is how many points you want the polynomials evaluated at. The ordinates of the points are placed in self.x. You may alternatively specify the points as argument x, in which case the x_() function will never be called.

Overrides: ortho.__init__
(inherited documentation)

### recurse(self, n, fn, fnm1)

source code

Does the recurrence relation, evaluating f_(n+1) as a function of n, f_n, and f_(n-1). For n=0 and n=1, fn and fnm1 may be None.

Overrides: ortho_poly.recurse
(inherited documentation)

### wt_(self)

source code
Overrides: ortho.wt_

 Class Variable Details

### __doc__

Value:
 ```"""Chebyshev polynomials of the second kind, orthonormal over (-1, 1) with weight (1-x^2)^(1/2). Called Un(x) in Abramowitz and Stegun. """ ```

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