An Analytical Expression for the Hubble diagram of supernovae and gamma-ray bursts

A recent paper by Harmut Traunm\"uller shows that the most adequate equation to interpret the observations on magnitude and redshift from 892 type 1a supernovae would be mu = 5 log[(1+z) ln(1+z)] + const. We discuss this result which is exacly the one we have obtained few years ago when postulating a relation between the speed of light and the expansion of the universe. We also compare our analytical result to the conclusion of Marosi who studied 280 supernovae and gamma-ray bursts in the range 0.1014 < z < 8.1. The difference between his results and ours is at worst of 0.3 %.