DLMF:14.5.E10 (Q4722)

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DLMF:14.5.E10
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    Statements

    Defining formula
    𝑸 1 ⁡ ( x ) = x 2 ⁢ ln ⁡ ( x + 1 x - 1 ) - 1 . shorthand-associated-Legendre-black-Q 1 𝑥 𝑥 2 𝑥 1 𝑥 1 1 {\displaystyle{\displaystyle\boldsymbol{Q}_{1}\left(x\right)=\frac{x}{2}\ln% \left(\frac{x+1}{x-1}\right)-1.}}
    0 references
    DLMF id
    DLMF:14.5.E10
    0 references
    Symbols used
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    Q11597
    Defining formula
    𝑸 ν ⁡ ( z ) = 𝑸 ν 0 ⁡ ( z ) shorthand-associated-Legendre-black-Q 𝜈 𝑧 associated-Legendre-black-Q 0 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}_{\NVar{\nu}}\left(\NVar{z}\right)=% \boldsymbol{Q}^{0}_{\nu}\left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m6aadec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1gdec
    0 references
     
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