Partition functions for two-dimensional Ising models using Generalised Hypergeometric series and Chebyshev polynomials

The zero-field partition function of two-dimensional nearest neighbor Ising models of square lattices is derived in terms of the generalized hypergeometric series by evaluating the integral in the exact solution of Onsager. An approximate equation for the partition function in terms of Chebyshev polynomials is also provided.