In analogy with the periods of abelian integrals of differentials of third
kind for an elliptic curve defined over a number field, we introduce a notion
of periods of third kind for a rank 2 Drinfeld Fq[t]-module rho defined over an
algebraic function field and derive explicit formulae for them. When rho has
complex multiplication by a separable extension, we prove the algebraic
independence of rho-logarithms of algebraic points that are linearly
independent over the CM field of rho. Together with the main result in [CP08],
we completely determine all the algebraic relations among the periods of first,
second and third kinds for rank 2 Drinfeld Fq[t]-modules in odd characteristic.