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Spherical Harmonics: Difference between revisions
→Associated Legendre Polynomials
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===Associated Legendre Polynomials=== | ===Associated Legendre Polynomials=== | ||
{{main | Wikipedia:Associated Legendre polynomials}} | {{main | Wikipedia:Associated Legendre polynomials}} | ||
Associated Legendre Polynomials are a set of orthogonal polynomials defined over \([-1, 1]\). | Associated Legendre Polynomials are a set of orthogonal polynomials defined over \([-1, 1]\). | ||
Each is represented as \(P^m_l\) where \(0 \leq m \leq l\). | |||
I.e. | |||
\(P^0_0(x)\) | |||
\(P^0_1(x), P^1_1(x)\) | |||
\(P^0_2(x), P^1_2(x),p^2_2(x)\) | |||
The following 3 recurrance relations define the associated legendre polynomials: | The following 3 recurrance relations define the associated legendre polynomials: | ||