I find it quite intriguing that I can generate a lot of special functions, my questions are as follows:

1. Is there any limit on the number of special functions?

2. What current literature in applied and rigorous Special Functions can you recommend me?

3. I looked at the integral $$\int \frac{log x}{Ei(x)}$$ in mathematica, and there doesn't seem to be a lot of information regarding this function, does it have any applications in analysis or mathematical physics?

   Thanks in advance.