The use of weighting functions in stellar model atmospheres.

The Unsold (1955) weighting function used in analytical models of stellar atmospheres is shown to yield an improved approximation to the exponential integral. The function is considered in terms of a simplified stellar atmosphere with continuous and selective line opacities caused by pure absorption. It is demonstrated that a weighting function used by de Jager and Neven (1967) involves a flux integral and results in an approximation that is only 10 percent accurate. The exponential integral-based weighting function is calculated to be more accurate by a factor of the square root of 3.