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16 May 2024
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22:02 | Generating Function for Legendre Polynomials 4 changes history +481 [Prime.mover (4×)] | |||
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22:02 (cur | prev) 0 Prime.mover talk contribs | |||
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22:02 (cur | prev) 0 Prime.mover talk contribs | |||
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19:03 (cur | prev) −16 Prime.mover talk contribs | ||||
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15:45 (cur | prev) +497 Prime.mover talk contribs | ||||
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N 17:55 | Length of Legendre Polynomial 2 changes history +3,158 [Prime.mover (2×)] | |||
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17:55 (cur | prev) +1 Prime.mover talk contribs | |||
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17:24 (cur | prev) +3,157 Prime.mover talk contribs (Created page with "== Theorem == <onlyinclude> Let $\map {P_n} x$ denote the '''Legendre polynomial of order $n$'''. Let $\norm {\map {P_n} x}$ denote the '''length''' of $\map {P_n} x$. Then: :$\norm {\map {P_n} x} := \sqrt {\frac 2 {2 n + 1} }$ </onlyinclude> == Proof == Applying Bonnet's Recursion Formula for $n - 1$: :$n \map {P_n} x = \paren {2 n - 1} x \map {P_{n - 1} } x - \paren {n - 1} \map {...") | |||
| N 17:34 | Category:Examples of Legendre Polynomials diffhist +80 Prime.mover talk contribs (Created page with "{{ExampleCategory|def = Legendre Polynomial}} Category:Legendre Polynomials") | ||||
| N 16:44 | Category:Associated Legendre Functions diffhist +129 Prime.mover talk contribs (Created page with "{{SubjectCategory|Associated Legendre Function}} Category:Legendre Polynomials Category:Legendre's Differential Equation") | ||||
| N 16:31 | Bonnet's Recursion Formula diffhist +396 Prime.mover talk contribs (Created page with "== Theorem == <onlyinclude> Let $\map {P_n} x$ denote the Legendre polynomial of order $n$. '''Bonnet's Recursion Formula''' states: :$\paren {n + 1} \map {P_{n + 1} } x = \paren {2 n + 1} x \map {P_n} x - n \map {P_{n - 1} } x$ </onlyinclude> == Proof == {{ProofWanted}} {{Namedfor|Pierre Ossian Bonnet|cat = Bonnet}} Category:Legendre Polynomials") | ||||