DLMF:14.17.E20 (Q4901): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1aedec

Revision as of 13:26, 2 January 2020

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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}}}
    0 references
    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
     
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