Is memorization bad or good in this case? Is it even necessary?

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When (self)learning quantum mechanics, I was introduced to Hermitian polynomials when learning about harmonic oscillators. This was pretty simple to remember, but then, today, when I first started reading about 3D quantum mechanics (when the Schroedinger equation has now become spherical), I am being attacked by differential equations which have *very* strange solutions... some of them include the spherical harmonics, associated Legendre functions (with Legendre polynomials), Bessel spherical functions, and Neumann spherical functions.

In a quantum mechanics undergraduate course, are such formulae provided (to avoid memorization)?
 
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When I took quantum mechanics, I did not have to know "Legendre functions (with Legendre polynomials), Bessel spherical functions, and Neumann spherical functions" too thoroughly. As I recall, I was just learning Bessel, Neumann, and Legendre functions.

The answer might depend on your learning style. I learn things from the top down. I get the big picture first, and then dig down into the finer (and more finer) details. If it were me I would just focus on the quantum mechanics and learn what ever mathematical details it required.