shifted_chebyshev_polynomial_v

→Tensor

shifted_chebyshev_polynomial_v(x: Tensor, n: int)

source

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

Chebyshev V polynomials of the third kind composed with $x \mapsto 2x - 1$ , yielding a basis orthogonal on $[0, 1]$ .

Parameters

xTensor

Argument on

[0, 1]

; any floating-point dtype.

nint

Non-negative polynomial degree.

Returns

Tensor

$V^*_n(x) = V_n(2x - 1)$ , element-wise.

Notes

$V^*_n(x) = V_n(2x - 1)$ .

Examples

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