DLMF:14.5.E29 (Q4741)

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DLMF:14.5.E29
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    Statements

    Defining formula
    𝖰 2 ⁡ ( x ) = 3 ⁢ x 2 - 1 4 ⁢ ln ⁡ ( 1 + x 1 - x ) - 3 2 ⁢ x , shorthand-Ferrers-Legendre-Q-first-kind 2 𝑥 3 superscript 𝑥 2 1 4 1 𝑥 1 𝑥 3 2 𝑥 {\displaystyle{\displaystyle\mathsf{Q}_{2}\left(x\right)=\frac{3x^{2}-1}{4}\ln% \left(\frac{1+x}{1-x}\right)-\frac{3}{2}x,}}
    0 references
    DLMF id
    DLMF:14.5.E29
    0 references
    Symbols used
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2addec
    0 references
    Q11596
    Defining formula
    𝖰 ν ⁡ ( x ) = 𝖰 ν 0 ⁡ ( x ) shorthand-Ferrers-Legendre-Q-first-kind 𝜈 𝑥 Ferrers-Legendre-Q-first-kind 0 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{Q}^{0}_{\nu}\left(x\right)}}
    xml-id
    C14.S2.SS2.p2.m4addec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1idec
    0 references
     
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