Question: Maple 14: Using sequences, arrays

Though I have been a casual Maple user since M12, I really don't know how to use it well, and am just learning it. I set myself a few tasks to help me discover its potential. I find that I learn better if I have some goal, even if it is just a sample goal.

In the accompanying file, I want to see how to use M14, and explore how to use Legendre polynomials.

Q: In (3.4), is there a cleaner way to declare the sequence?

Q: Am I using sequences correctly in this file?

I am trying to duplicate the material that is shown in the accompanying PDF file, where the plot actually comes from the calculations, much as I am trying to do with Maple 14.

Q: (3.9) gets the correct coefs, but not very pretty...is there a better way?

Q: I eventually stumbled upon (3.10), which looks correct, but when I dragged it to the plot and dropped it, I got only the first Legendre polynomial, not n of them. How do I get that?

Q: How do I show that I dropped L on the plot? The legend shows Curve 1 and 2.

Q: Is there a way to combine (3.8) and (3.9) into one stem, for example, by using array subscripts? I tried and failed.

Legendre_polynomial_.mw

Legendre_polynomial_.pdf