Accurate free-free Gaunt factors for astrophysical plasmas

New calculations of free-free transition matrix element integrals are performed using modern symbolic computing techniques to evaluate the hypergeometric functions with complex arguments. The results are presented in both graphical and tabular form including accurate extrapolation methods. The results are accurate to the level of similar to 10(-4), beyond which relativistic corrections would be needed, which are not included. The results are also computed over a very wide range of scaled ionic temperature (gamma(2)) and wavelength, extending earlier results to new regimes encountered in highly photoionized and non-equilibrium ionization plasmas. These results will be useful in the spectral range from submillimetre to hard X-ray wavelengths and temperatures from 10 to 10(9) K.