DLMF:14.17.E8 (Q4889): Difference between revisions

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Property / constraint
 

m > 0 𝑚 0 {\displaystyle{\displaystyle m>0}}

m>0
Property / constraint: m > 0 𝑚 0 {\displaystyle{\displaystyle m>0}} / rank
 
Normal rank

Revision as of 17:53, 30 December 2019

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DLMF:14.17.E8
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    Statements

    - 1 1 𝖯 n l ( x ) 𝖯 n m ( x ) 1 - x 2 d x = ( n + m ) ! ( n - m ) ! m δ l , m , superscript subscript 1 1 Ferrers-Legendre-P-first-kind 𝑙 𝑛 𝑥 Ferrers-Legendre-P-first-kind 𝑚 𝑛 𝑥 1 superscript 𝑥 2 𝑥 𝑛 𝑚 𝑛 𝑚 𝑚 Kronecker 𝑙 𝑚 {\displaystyle{\displaystyle\int_{-1}^{1}\frac{\mathsf{P}^{l}_{n}\left(x\right% )\mathsf{P}^{m}_{n}\left(x\right)}{1-x^{2}}\mathrm{d}x=\frac{(n+m)!}{(n-m)!m}% \delta_{l,m},}}
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    DLMF:14.17.E8
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    m > 0 𝑚 0 {\displaystyle{\displaystyle m>0}}
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