For the Schechter luminosity function of galaxies (Equation 12.21), find the number density of galaxies more luminous than L, as a function of L∗, Φ∗, and α. In the limit L→0, show why α=−1 leads to problems, mathematically speaking. What is a plausible physical solution to this mathematical problem? [Hint: an acquaintance with incomplete gamma functions will be useful.]