code: def healpix_to_lonlat(healpix_index, nside, dx=None, dy=None, order='ring'):
      
  
      _validate_nside(nside)
  
      if _validate_order(order) == 'ring':
          func = _core.healpix_ring_to_lonlat
      else:  # _validate_order(order) == 'nested'
          func = _core.healpix_nested_to_lonlat
  
      if dx is None:
          dx = 0.5
      else:
          _validate_offset('x', dx)
      if dy is None:
          dy = 0.5
      else:
          _validate_offset('y', dy)
  
      nside = np.asarray(nside, dtype=np.intc)
  
      lon, lat = func(healpix_index, nside, dx, dy)
  
      lon = Longitude(lon, unit=u.rad, copy=False)
      lat = Latitude(lat, unit=u.rad, copy=False)
  
      return lon, lat
docs: Convert HEALPix indices (optionally with offsets) to longitudes/latitudes.
  
      If no offsets (``dx`` and ``dy``) are provided, the coordinates will default
      to those at the center of the HEALPix pixels.
  
      Parameters
      ----------
      healpix_index : int or `~numpy.ndarray`
          HEALPix indices (as a scalar or array)
      nside : int or `~numpy.ndarray`
          Number of pixels along the side of each of the 12 top-level HEALPix tiles
      dx, dy : float or `~numpy.ndarray`, optional
          Offsets inside the HEALPix pixel, which must be in the range [0:1],
          where 0.5 is the center of the HEALPix pixels (as scalars or arrays)
      order : { 'nested' | 'ring' }, optional
          Order of HEALPix pixels
  
      Returns
      -------
      lon : :class:`~astropy.coordinates.Longitude`
          The longitude values
      lat : :class:`~astropy.coordinates.Latitude`
          The latitude values