How do I obtain a set of orthogonal polynomials up to the 7th term?

[Barracuda]

Hello everyone,
I need some help with this solution. I'm trying to obtain a set of orthogonal polynomials up to the 7th term. I think i got it up to the 6th term, but the integration is getting more complex. I'm not sure if I'm on the right track. Please help

 

[Barracuda]

 

[Keith_McClary]

Could you write the recursion relation, preferably in Latex?

 

[phyzguy]

Nobody wants to wade through your hand-written figures. If you want a response, you're going to have to learn how to enter it into latex.

 

[Infrared]

I haven't read your images, but it seems to me like you're describing the Legendre polynomials (https://en.wikipedia.org/wiki/Legen...ition_by_construction_as_an_orthogonal_system). If so, you can check your work there.

Is there a reason you have to do this calculation by hand (instead of using a computer)? I would expect it to be very tedious.

 

[Barracuda]

I haven't read your images, but it seems to me like you're describing the Legendre polynomials (https://en.wikipedia.org/wiki/Legen...ition_by_construction_as_an_orthogonal_system). If so, you can check your work there.

Is there a reason you have to do this calculation by hand (instead of using a computer)? I would expect it to be very tedious.

I'm using Gram-Schmidt. I'll type it out using Latex

 

[Keith_McClary]

If you mean typing out all your handwriting, first please explain why you seem to be doing it the hard way (rather than using the recurrence relation for example).