DLMF:14.3.E11 (Q4700)

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DLMF:14.3.E11
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    Statements

    test
    𝖯 ν μ ⁡ ( x ) = cos ⁡ ( 1 2 ⁢ ( ν + μ ) ⁢ π ) ⁢ w 1 ⁢ ( ν , μ , x ) + sin ⁡ ( 1 2 ⁢ ( ν + μ ) ⁢ π ) ⁢ w 2 ⁢ ( ν , μ , x ) , Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 1 2 𝜈 𝜇 𝜋 subscript 𝑤 1 𝜈 𝜇 𝑥 1 2 𝜈 𝜇 𝜋 subscript 𝑤 2 𝜈 𝜇 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\mu}_{\nu}\left(x\right)=\cos\left(% \tfrac{1}{2}(\nu+\mu)\pi\right)w_{1}(\nu,\mu,x)+\sin\left(\tfrac{1}{2}(\nu+\mu% )\pi\right)w_{2}(\nu,\mu,x),}}
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    DLMF id
    DLMF:14.3.E11
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    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.m2acdec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
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    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1jdec
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    Q11591
    test
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1fdec
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    Q11590
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1idec
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    Q11594
    test
    w 2 subscript 𝑤 2 {\displaystyle{\displaystyle w_{2}}}
    xml-id
    C14.S3.XMD1.m1dec
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