Laguerre Polynomials link to the Schrodinger Equation

I was wondering if anyone could help me. I'm struggling to come to the solution regarding Laguerre polynomials for determining the radial component to insert into the Schrodinger equation.

I know it's similar to determining the Hermite and Legendre polynomials and I found those to be okay.

I'm struggling from slide 10 onwards in the first attachment and was wondering if anyone was able to help talk me through it or if someone knows a decent textbook on Laguerre polynomials. The recommended textbook for the course (Brandsen and Jochiam Quantum Mechanics) doesn't really help explain it.

Just realised my attachments haven't linked with my original post - I can only assume they were too large.

Okay I'll have a look at that thanks! I had a look at the Math Methods book for science and engineering but it's a bit too vague so will have a look at the one you've suggested.

Well I'm looking at it from a physicist's perspective so the deep maths has been avoided on the course and it is purely the application of the polynomials in determining specific values for energy levels in an atomic system. There is a maths course available which goes into the detail for physicists at my uni but I can't take it due to other course requirements unfortunately.