DLMF:14.9.E17 (Q4809)

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DLMF:14.9.E17
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    Statements

    test
    P ν μ ⁡ ( x ) = ( 2 / π ) 1 / 2 ⁢ ( x 2 - 1 ) - 1 / 4 ⁢ 𝑸 - μ - ( 1 / 2 ) ν + ( 1 / 2 ) ⁡ ( x ⁢ ( x 2 - 1 ) - 1 / 2 ) . Legendre-P-first-kind 𝜇 𝜈 𝑥 superscript 2 𝜋 1 2 superscript superscript 𝑥 2 1 1 4 associated-Legendre-black-Q 𝜈 1 2 𝜇 1 2 𝑥 superscript superscript 𝑥 2 1 1 2 {\displaystyle{\displaystyle P^{\mu}_{\nu}\left(x\right)=(2/\pi)^{1/2}\left(x^% {2}-1\right)^{-1/4}\*\boldsymbol{Q}^{\nu+(1/2)}_{-\mu-(1/2)}\left(x\left(x^{2}% -1\right)^{-1/2}\right).}}
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    DLMF id
    DLMF:14.9.E17
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    Symbols used
    Q11481
    test
    P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m1aedec
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    Q11592
    test
    𝑸 ν μ ⁡ ( z ) associated-Legendre-black-Q 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m3addec
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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.m2ajdec
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