DLMF:34.3.E21 (Q9736)

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DLMF:34.3.E21
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    Statements

    Defining formula
    ∫ 0 π P l 1 ⁡ ( cos ⁡ θ ) ⁢ P l 2 ⁡ ( cos ⁡ θ ) ⁢ P l 3 ⁡ ( cos ⁡ θ ) ⁢ sin ⁡ θ ⁢ d θ = 2 ⁢ 3 ⁢ j ⁢ l 1 ⁢ l 2 ⁢ l 3 ⁢ 000 2 , superscript subscript 0 𝜋 shorthand-Legendre-P-first-kind subscript 𝑙 1 𝜃 shorthand-Legendre-P-first-kind subscript 𝑙 2 𝜃 shorthand-Legendre-P-first-kind subscript 𝑙 3 𝜃 𝜃 𝜃 2 threej subscript 𝑙 1 subscript 𝑙 2 subscript 𝑙 3 superscript 000 2 {\displaystyle{\displaystyle\int_{0}^{\pi}P_{l_{1}}\left(\cos\theta\right)P_{l% _{2}}\left(\cos\theta\right)P_{l_{3}}\left(\cos\theta\right)\sin\theta\mathrm{% d}\theta=2\mathit{3j}{l_{1}}{l_{2}}{l_{3}}{0}{0}{0}^{2},}}
    0 references
    DLMF id
    DLMF:34.3.E21
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
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    Q11447
    Defining formula
    P ν ⁡ ( z ) = P ν 0 ⁡ ( z ) shorthand-Legendre-P-first-kind 𝜈 𝑧 Legendre-P-first-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m3aadec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    $$\mathit{3j}$$ symbol
    Defining formula
    3 ⁢ j ⁢ j 1 ⁢ j 2 ⁢ j 3 ⁢ m 1 ⁢ missing threej subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑚 1 missing {\displaystyle{\displaystyle\mathit{3j}{\NVar{j_{1}}}{\NVar{j_{2}}}{\NVar{j_{3% }}}{\NVar{m_{1}}}{\NVar{missing}\)\@add@PDF@RDFa@triples\end{document}}}}
    xml-id
    C34.S2.E4.m2asdec
    0 references
    Q12713
    Defining formula
    l , l r 𝑙 subscript 𝑙 𝑟 {\displaystyle{\displaystyle l,l_{r}}}
    xml-id
    C34.S1.XMD2.m1bdec
    0 references
     
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