In this paper two sets of improved approximate expressions of emissivity $$\eta _\nu /BN $$ , absorptivity $$\kappa _\nu B/N $$ , effective temperature Teff, and frequency of peak brightness ν_p of gyrosynchrotron radiation are presented respectively for the ranges from 5 to 10 and 10 to 100 of harmonic numbers s(= ν/ν_B). The expressions are designed for the range from 20° to 80° of viewing angle θ, and the range 2 to 7 of electron energy spectral index δ. They are expressed by a power-law function in which the indexes are fitted by polynomial expressions of δ. Their statistical errors are, respectively, 24% and 32% for $$\eta _\nu /BN $$ and $$\kappa _\nu B/N $$ for $$5 \leqslant \nu /\nu _B \leqslant 10,{\text{ }}22\% $$ and 28% for $$10 \leqslant \nu /\nu _B \leqslant 100 $$ . Their accuracies are much better than those of linear fitting of the power-law index.