DLMF:14.5.E30 (Q4742)

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DLMF:14.5.E30
No description defined

    Statements

    Defining formula
    𝑸 2 ⁡ ( x ) = 3 ⁢ x 2 - 1 8 ⁢ ln ⁡ ( x + 1 x - 1 ) - 3 4 ⁢ x . shorthand-associated-Legendre-black-Q 2 𝑥 3 superscript 𝑥 2 1 8 𝑥 1 𝑥 1 3 4 𝑥 {\displaystyle{\displaystyle\boldsymbol{Q}_{2}\left(x\right)=\frac{3x^{2}-1}{8% }\ln\left(\frac{x+1}{x-1}\right)-\frac{3}{4}x.}}
    0 references
    DLMF id
    DLMF:14.5.E30
    0 references
    Symbols used
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aedec
    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.m6addec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1jdec
    0 references
     
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