I just had a few questions not directly addressed in my textbook, and they're a little odd so I thought I would ask, if you don't mind. :)(adsbygoogle = window.adsbygoogle || []).push({});

-Firstly, I was just wondering, why is it that Legendre polynomials are only evaluated on a domain of {-1. 1]? In realistic applications, is this a limiting factor? Is there a way to find solutions for a larger domain?

-Why exactly must n > -1?

Is there a particular reason why it's only evaluated for these values of n? Is there an another approach for n < -1? Also, must n be a a non-negative integer or can n be any real number greater than -1?

-Is there a relatively short proof to prove ## \int _{-1}^1 P_m P_n = \frac {2}{2n+1}; m = n ##? All the ones I've seen are quite long and tedious, and are not as intuitive as the other case for ## m \neq n ##. I was just curious since I could not seem to find one.

Also, as a side question: what exactly happens to matrices that undergo elementary row operations? I know the column space is distorted and the row space is intact for elementary row operations, but what exact properties are now the same and different between a matrix A and a matrix A' derived from elementary row operations on A?

Also, why is it necessary Legendre polynomials pass through the point (1,1)? Why is this point unique?

Sorry for the questions! A few that were just lingering in my head that I wanted to address. Thank you!

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# Details regarding Legendre Polynomials

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