  We present the results of calculations of the $p^4$ and $p^6$ order
low-energy constants for the chiral Lagrangian with tensor sources for both two
and three flavors of pseudoscalar mesons. This is a generalization of our
previous work on similar calculations without tensor sources in terms of the
quark self-energy $\Sigma(p^2)$, based on the first principle derivation of the
low-energy effective Lagrangian and computation of the low-energy constants
with some rough approximations. With the help of partial integration and some
epsilon relations, we find that some $p^6$ order operators with tensor sources
appearing in the literature are related to each other. That leaves 98
independent terms for $n$-flavor, 92 terms for three-flavor, and 65 terms for
two-flavor cases. We also find that the odd-intrinsic-parity chiral Lagrangian
with tensor sources cannot independently exist in any order of low-energy
expansion.
