Constraints on the luminosity function of gamma-ray bursts detected by BATSE

We have utilized the integral moment analysis technique of Horack & Emslie to extract information on the allowable form of the luminosity function for gamma-ray bursts observed by Burst and Transient Source Experiment (BATSE). Using the general properties of moments, we are able to derive constraints on the range of luminosity from which the gamma-ray bursts must be sampled. These constraints are independent of the form of the radial distribution of the gamma-ray bursts, and depend only on the assumptions that space is Euclidean and that the luminosity function phi(L) is distance independent. For power-law luminosity functions of the form phi(L) = A(sub 0)L(exp -alpha), we find that the range of luminosity from which 80% of the gamma-ray bursts must be sampled cannot exceed approximately 6.5, with a 3 sigma upper limit of 12-15, regardless of the value of alpha.