DLMF:14.2.E6 (Q4684)

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DLMF:14.2.E6
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    Statements

    Defining formula
    𝒲 ⁡ { 𝖯 ν - μ ⁡ ( x ) , 𝖰 ν μ ⁡ ( x ) } = cos ⁡ ( μ ⁢ π ) 1 - x 2 , Wronskian Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 𝜇 𝜋 1 superscript 𝑥 2 {\displaystyle{\displaystyle\mathscr{W}\left\{\mathsf{P}^{-\mu}_{\nu}\left(x% \right),\mathsf{Q}^{\mu}_{\nu}\left(x\right)\right\}=\frac{\cos\left(\mu\pi% \right)}{1-x^{2}},}}
    0 references
    DLMF id
    DLMF:14.2.E6
    0 references
    Symbols used
    Ferrers function of the first kind
    Defining formula
    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
    0 references
    Ferrers function of the second kind
    Defining formula
    𝖰 ν μ ⁡ ( x ) Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E2.m2abdec
    0 references
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3abdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
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    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1edec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1ddec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1edec
    0 references
     
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