Earlier quoted context omitted.
I can't, but I bet they have a standard and well-accepted definition in the mathematical community. In fact, pretty much any real-valued mathematical function passes the test. The interface is settled, almost by definition since C++ functions are inspired by mathematical functions: pass in arguments, return result. Use range/domain exceptions or NaN for reporting such errors. The semantics are obvious: compute the na…
There’s nearly a limitless amount of standard and well-defined functions with a single usage, like those. There’s hardly a point in implementing them in the standard library and C++ is the only language that I’m aware of that has those. If the goal was to create a specialized library for solving differential equations, those would be handy there. But if not, even if you tried implementing everything that you could po…
Why do these functions bother you so much? It can't be namespace pollution; they're under std::. It can't be that you disagree with their interface or semantics, since by your own admission you don't even know what they are.
You named some other features, such as quaternions, that you think would be better for implementors to spend their time on, but surely you can imagine someone like yourself who is tired of having to define the Bessel functions every time they start a new project, and can't imagine why the C++ committee saw fit to include something so useless and obscure as quaternions before getting to Bessel functions.