DLMF:14.5.E12 (Q4724)

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DLMF:14.5.E12
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    Statements

    Defining formula
    𝖯 ν - 1 / 2 ⁡ ( cos ⁡ θ ) = ( 2 π ⁢ sin ⁡ θ ) 1 / 2 ⁢ sin ⁡ ( ( ν + 1 2 ) ⁢ θ ) ν + 1 2 , Ferrers-Legendre-P-first-kind 1 2 𝜈 𝜃 superscript 2 𝜋 𝜃 1 2 𝜈 1 2 𝜃 𝜈 1 2 {\displaystyle{\displaystyle\mathsf{P}^{-1/2}_{\nu}\left(\cos\theta\right)=% \left(\frac{2}{\pi\sin\theta}\right)^{1/2}\frac{\sin\left(\left(\nu+\frac{1}{2% }\right)\theta\right)}{\nu+\frac{1}{2}},}}
    0 references
    DLMF id
    DLMF:14.5.E12
    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
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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.m2aedec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
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    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1edec
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    Q11598
    Defining formula
    0 < θ < π 0 𝜃 𝜋 {\displaystyle{\displaystyle 0<\theta<\pi}}
    xml-id
    C14.S5.XMD2.m1adec
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