  An analytical model is proposed to determine the expressions of the
semiconductor optical gain coefficient by using the special functions. These
expressions differ from the standard numerical calculations approaches and they
involve sums of the polylogarithm and incomplete gamma functions. One of the
calculation results presented here reproduces formulae developed in the study.
The new formulae obtained here provide a sufficient way to calculate the
semiconductor optical gain on the total carrier density and temperature in the
semiconductor lasers. The obtained analytical expression gives an accurate and
precise evaluation of the semiconductor gain function. The performance of the
proposed formula is confirmed by its implementation of the different values of
the parameter. The sufficiency obtained results of this approach was confirmed
by the other literature data.
