DLMF:14.17.E17 (Q4898)

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DLMF:14.17.E17
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    Statements

    test
    ∫ 0 π 𝖰 l ⁡ ( cos ⁡ θ ) ⁢ 𝖯 m ⁡ ( cos ⁡ θ ) ⁢ 𝖯 n ⁡ ( cos ⁡ θ ) ⁢ sin ⁡ θ ⁢ d θ = 0 , superscript subscript 0 𝜋 shorthand-Ferrers-Legendre-Q-first-kind 𝑙 𝜃 shorthand-Ferrers-Legendre-P-first-kind 𝑚 𝜃 shorthand-Ferrers-Legendre-P-first-kind 𝑛 𝜃 𝜃 𝜃 0 {\displaystyle{\displaystyle\int_{0}^{\pi}\mathsf{Q}_{l}\left(\cos\theta\right% )\mathsf{P}_{m}\left(\cos\theta\right)\mathsf{P}_{n}\left(\cos\theta\right)% \sin\theta\mathrm{d}\theta=0,}}
    0 references
    DLMF id
    DLMF:14.17.E17
    0 references
    constraint
    | m - n | < l < m + n 𝑚 𝑛 𝑙 𝑚 𝑛 {\displaystyle{\displaystyle|m-n|<l<m+n}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
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    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2acdec
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