Yes, good point. I was actually thinking about special functions and that they are usually defined through differential equations (so, yeah, I more or less stol

Yes, good point. I was actually thinking about special functions and that they are usually defined through differential equations (so, yeah, I more or less stole the idea from there and did not cite it properly :-/ but I did not want to bring all of that in to my comment). Thanks for elaborating on this.