shifted_chebyshev_polynomial_w

→Tensor

shifted_chebyshev_polynomial_w(x: Tensor, n: int)

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Shifted Chebyshev W polynomial $W^*_n(x)$ on $[0, 1]$ .

Chebyshev W polynomials of the fourth kind composed with $x \mapsto 2x - 1$ .

Parameters

xTensor

Argument on

[0, 1]

; any floating-point dtype.

nint

Non-negative polynomial degree.

Returns

Tensor

$W^*_n(x) = W_n(2x - 1)$ , element-wise.

Notes

$W^*_n(x) = W_n(2x - 1)$ .

Examples

>>> import lucid
>>> from lucid.special import shifted_chebyshev_polynomial_w
>>> shifted_chebyshev_polynomial_w(lucid.tensor([0.0, 1.0]), n=1)
Tensor([-1.0000, 3.0000])

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