There are a lot of special functions, and I wonder if there is a website that collects all of them, similar to how the Encyclopedia of Triangle Centers collects information on triangle centers.
Another question is: What are the criteria for defining a new special function? One can define anything if they want to, so is there any established criteria for what would be considered and accepted as a new special function?
For example I can just define a function like $\Theta(x)$ to be the inverse function for $e^{\sin(x)}\cos(x)+ 5x^x-\Gamma(\gamma x) $ where $x\in [0, \frac \pi 2 ]$ Now this is a new function, what one should do to make similar functions an "acceptable" special function? I think a function to be considered a new one is that it can't be obtained via definite combinations of the known functions.
In geometry if one discovers a new triangle center he can just submit it to ETC I wonder if a similar thing exist for special functions?
It seems like the such websites don't exist but I think a websites that collects special functions like how ETC collect triangle centers is a good idea that I want to make this website but I don't have enough knowledge in mathematics or programming to make such thing I wonder whether I can request such Idea in MSE or MO for the community ton do.