Virial expansion and condensation with a new generating function

Mayer's convergence method for virial expansion and condensation is studied using a new generating function for canonical partition function, which directly depends on irreducible cluster integral, $\beta_k$, unlike Mayer's work where it depends on reducible cluster integral, $b_l$. The virial expansion, criteria for it's validity and criteria for condensation, etc. are derived from our generating function. All earlier Mayer's results are obtained from this new generating function.