I have learnt how to use trig functions, hyperbolic trig functions, exponentials and logs and simple things like polynomials, ellipses, hyperbolas and rational functions but lately when doing calculus I have found that many problems in differential equations and integration cannot be done using the functions I know. I would like to learn a few more functions but I don't know which ones are the most useful and which are at my level. I was thinking of things like the gamma function or Bessel functions for instance.
Basically, what are the most useful functions I didn't list in the first sentence. It would be best if they have applications in physics.