Just a question I am having trouble understanding. I have the Schechter luminosity function for galaxies, given as:
$$Phi(L)dL=Phi_{0}left({frac{L}{L_{star}}}right)^{alpha}e^{-frac{L}{L_{star}}}frac{dL}{L_{star}}$$
I need to consider the case when $alpha=-1$. And then show that the average luminosity of a galaxy is exactly $L_{star}$. Could somebody explain how I could go about doing this and perhaps a hint or some part of a setup would be excellent. I really need to understand this.
Another part, which is related to the above question, is asking me to explain why the total luminosity is a finite number, whereas the total number of galaxies diverges. By this does it mean that the total number is infinite? Any extra comments on this would also be really appreciated.
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