DLMF:14.5.E1 (Q4713)

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DLMF:14.5.E1
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    Statements

    Defining formula
    𝖯 ν μ ⁡ ( 0 ) = 2 μ ⁢ π 1 / 2 Γ ⁡ ( 1 2 ⁢ ν - 1 2 ⁢ μ + 1 ) ⁢ Γ ⁡ ( 1 2 - 1 2 ⁢ ν - 1 2 ⁢ μ ) , Ferrers-Legendre-P-first-kind 𝜇 𝜈 0 superscript 2 𝜇 superscript 𝜋 1 2 Euler-Gamma 1 2 𝜈 1 2 𝜇 1 Euler-Gamma 1 2 1 2 𝜈 1 2 𝜇 {\displaystyle{\displaystyle\mathsf{P}^{\mu}_{\nu}\left(0\right)=\frac{2^{\mu}% \pi^{1/2}}{\Gamma\left(\frac{1}{2}\nu-\frac{1}{2}\mu+1\right)\Gamma\left(\frac% {1}{2}-\frac{1}{2}\nu-\frac{1}{2}\mu\right)},}}
    0 references
    DLMF id
    DLMF:14.5.E1
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
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    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.m2adec
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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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    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1dec
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    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1dec
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