DLMF:14.17.E20 (Q4901)

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DLMF:14.17.E20
No description defined

    Statements

    Defining formula
    ∫ 1 ∞ ( Q ν ⁡ ( x ) ) 2 ⁢ d x = ψ ′ ⁡ ( ν + 1 ) 2 ⁢ ν + 1 , superscript subscript 1 superscript shorthand-Legendre-Q-second-kind 𝜈 𝑥 2 𝑥 diffop digamma 1 𝜈 1 2 𝜈 1 {\displaystyle{\displaystyle\int_{1}^{\infty}(Q_{\nu}\left(x\right))^{2}% \mathrm{d}x=\frac{\psi'\left(\nu+1\right)}{2\nu+1},}}
    0 references
    DLMF id
    DLMF:14.17.E20
    0 references
    constraint
    ℜ ⁡ ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}
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    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1asdec
    0 references
    psi (or digamma) function
    Defining formula
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2agdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3asdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aedec
    0 references
    Q11448
    Defining formula
    Q ν ⁡ ( z ) = Q ν 0 ⁡ ( z ) shorthand-Legendre-Q-second-kind 𝜈 𝑧 Legendre-Q-second-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}% \left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m5abdec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1rdec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1mdec
    0 references
     
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