def METHOD_NAME(l: int, alpha: torch.Tensor) -> torch.Tensor:
    r""":math:`S^l(\alpha)` of `spherical_harmonics_alpha_beta`
    Parameters
    ----------
    l : int
        degree of the spherical harmonics.
    alpha : `torch.Tensor`
        tensor of shape ``(...)``.
    Returns
    -------
    `torch.Tensor`
        a tensor of shape ``(..., 2l+1)``
    """
    alpha = alpha.unsqueeze(-1)  # [..., 1]
    m = torch.arange(1, l + 1, dtype=alpha.dtype, device=alpha.device)  # [1, 2, 3, ..., l]
    cos = torch.cos(m * alpha)  # [..., m]
    m = torch.arange(l, 0, -1, dtype=alpha.dtype, device=alpha.device)  # [l, l-1, l-2, ..., 1]
    sin = torch.sin(m * alpha)  # [..., m]
    out = torch.cat(
        [
            math.sqrt(2) * sin,
            torch.ones_like(alpha),
            math.sqrt(2) * cos,
        ],
        dim=alpha.ndim - 1,
    )
    return out  # [..., m]