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

• Barracuda
In summary, the conversation is about obtaining a set of orthogonal polynomials up to the 7th term. The person is unsure if they are on the right track and is seeking help. They mention using Gram-Schmidt and ask for the recursion relation to be written in Latex. It is suggested to use a computer instead of doing the calculation by hand. The Legendre polynomials are mentioned as a reference for checking the work. The person is then asked to explain why they are doing it the hard way instead of using a recurrence relation.

#### 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

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Could you write the recursion relation, preferably in Latex?

sysprog
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.

sysprog, Barracuda, Mayhem and 1 other person
sysprog and Barracuda
Infrared said:
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

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).

sysprog