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authoredFeb 6, 2021
oopsy, monic != monomial
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‎_posts/2020-08-23-simplexquads.md

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@@ -24,7 +24,7 @@ Why bother with Legendre Polynomials? They have a number of great properties tha
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* They are a complete system (have good approximation properties for functions of lesser degree).
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* They exclude the end points (sometimes a negative).
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We will be working with normalised Legendre Polynomials (Monomials). That means that the value each polynomial is one at x=1. This has a number of consequences but the most useful one is that we can construct the sequence of polynomials up to degree n simply by applying the orthogonality condition.
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We will be working with normalised Legendre Polynomials (monic polynomials). That means that the value each polynomial is one at x=1. This has a number of consequences but the most useful one is that we can construct the sequence of polynomials up to degree n simply by applying the orthogonality condition.
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The first Legendre polynomial is the function equal to 1 everywhere on the interval [-1,1]. Then the next polynomial of one degree higher must be equal f(x)=x. In fact because of the first polynomial, all of the following polynomials will integrate to zero over the domain.
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