DLMF:14.3.E10 (Q4699): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11470 / rank
 
Normal rank
Property / Symbols used: Q11470 / qualifier
 
test:

Q ν μ ⁡ ( z ) Legendre-Q-second-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle Q^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\assLegendreQ[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Q11470 / qualifier
 
xml-id: C14.S21.SS1.p1.m2aadec

Revision as of 00:14, 2 January 2020

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DLMF:14.3.E10
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    Statements

    test
    𝑸 ν μ ⁡ ( x ) = e - μ ⁢ π ⁢ i ⁢ Q ν μ ⁡ ( x ) Γ ⁡ ( ν + μ + 1 ) . associated-Legendre-black-Q 𝜇 𝜈 𝑥 superscript 𝑒 𝜇 𝜋 𝑖 Legendre-Q-second-kind 𝜇 𝜈 𝑥 Euler-Gamma 𝜈 𝜇 1 {\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(x\right)=e^{-\mu% \pi i}\frac{Q^{\mu}_{\nu}\left(x\right)}{\Gamma\left(\nu+\mu+1\right)}.}}
    0 references
    DLMF id
    DLMF:14.3.E10
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2afdec
    0 references
    Q11470
    test
    Q ν μ ⁡ ( z ) Legendre-Q-second-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle Q^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m2aadec
    0 references
     
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