DLMF:14.17.E7 (Q4888): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10768 / rank
 
Normal rank
Property / Symbols used: Q10768 / qualifier
 
test:

δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}

\Kroneckerdelta{\NVar{j}}{\NVar{k}}
Property / Symbols used: Q10768 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r4.m5aadec

Revision as of 12:22, 2 January 2020

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DLMF:14.17.E7
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    Statements

    test
    ∫ - 1 1 𝖯 l m ⁡ ( x ) ⁢ 𝖯 n - m ⁡ ( x ) ⁢ d x = ( - 1 ) m l + 1 2 ⁢ δ l , n , superscript subscript 1 1 Ferrers-Legendre-P-first-kind 𝑚 𝑙 𝑥 Ferrers-Legendre-P-first-kind 𝑚 𝑛 𝑥 𝑥 superscript 1 𝑚 𝑙 1 2 Kronecker 𝑙 𝑛 {\displaystyle{\displaystyle\int_{-1}^{1}\mathsf{P}^{m}_{l}\left(x\right)% \mathsf{P}^{-m}_{n}\left(x\right)\mathrm{d}x=\frac{(-1)^{m}}{l+\frac{1}{2}}% \delta_{l,n},}}
    0 references
    DLMF id
    DLMF:14.17.E7
    0 references
    Symbols used
    Ferrers function of the first kind
    test
    𝖯 ν μ ⁡ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E1.m2afdec
    0 references
    Q10768
    test
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5aadec
    0 references
     
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