More details: The orbitals are the product of an Harmonic Orbital and a radial function. More details in https://en.wikipedia.org/wiki/Atomic_orbital#Types_of_orbita... and https://en.wikipedia.org/wiki/Hydrogen-like_atom#Non-relativ...

Note that this is the initial selection of orbitals. The "real"[1] orbitals are linear combinations of them. In some cases it's good enough to mix them using some easy combinations like in https://en.wikipedia.org/wiki/Orbital_hybridisation but in the general cases you must use a computer to calculate the best combination https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method .

[1] It get's more complicated.