Bilinear Expansion For Redistribution Functions

•A method for construction of a bilinear expansion for an angle-averaged redistribution function is suggested.•An eigenvalue and eigenvector determination problem is formulated.•The Voigt function and its derivatives are studied in detail.•Software package HAHMATH has been worked out.

We suggest here a method for construction of a bilinear expansion for an angle-averaged redistribution function. This function describes the elementary act of a photon scattering by a model two-level atom with the upper level broadened due to radiation damping. An eigenvalue and eigenvector determination problem is formulated and the relevant matrices are found analytically. Numerical procedures for their computations are elaborated as well. A simple method for the numerical calculations accuracy evaluation is suggested. It is shown that a family of redistribution functions describing the light scattering process within the spectral line frequencies can be constructed if the eigenvalue problem for the considered function is solved. It becomes possible if the eigenvalues and eigenvectors with the appropriate basic functions are used. The Voigt function and its derivatives used as basic functions are studied in detail as well.