  The short-distance coefficients for the color-octet ^3S_1 term in the
fragmentation function for a gluon to split into polarized heavy quarkonium
states are re-calculated to order alpha_s^2. The light-cone gauge remarkably
simplifies the calculation by eliminating many Feynman diagrams at the expense
of introducing spurious poles in loop integrals. We do not use any conventional
prescriptions for spurious pole. Instead, we only use gauge invariance with the
aid of Collins-Soper definition of the fragmentation function. Our result
agrees with a previous calculation of Braaten and Lee in the Feynman gauge, but
disagrees with another previous calculation.
