DLMF:14.9.E16 (Q4808)

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DLMF:14.9.E16
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    Statements

    Defining formula
    𝑸 ν μ ⁡ ( x ) = ( 1 2 ⁢ π ) 1 / 2 ⁢ ( x 2 - 1 ) - 1 / 4 ⁢ P - μ - ( 1 / 2 ) - ν - ( 1 / 2 ) ⁡ ( x ⁢ ( x 2 - 1 ) - 1 / 2 ) . associated-Legendre-black-Q 𝜇 𝜈 𝑥 superscript 1 2 𝜋 1 2 superscript superscript 𝑥 2 1 1 4 Legendre-P-first-kind 𝜈 1 2 𝜇 1 2 𝑥 superscript superscript 𝑥 2 1 1 2 {\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(x\right)=\left(% \tfrac{1}{2}\pi\right)^{1/2}\left(x^{2}-1\right)^{-1/4}\*P^{-\nu-(1/2)}_{-\mu-% (1/2)}\left(x\left(x^{2}-1\right)^{-1/2}\right).}}
    0 references
    DLMF id
    DLMF:14.9.E16
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    Symbols used
    Q11481
    Defining formula
    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.m1addec
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    Q11592
    Defining formula
    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.m3acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
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    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1odec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1ldec
    0 references
     
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