Torsion dependence of the covariant Taylor expansion in Riemann-Cartan space

We clarify the dependence on the torsion tensor of all coefficients in the covariant Taylor expansion of the HMDS coefficient in the heat kernel for the fermion of spin 1/2 in Riemann-Cartan space. The dependence on the torsion tensor of the quantities in the expansion coefficients is determined by the gamma matrices in the quantities, except for that of the matrix potential X itself. The quantities with gamma matrices contain the torsion tensor only in a peculiar form, and the others are independent of the torsion tensor.