DLMF:14.9.E4 (Q4794): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Ferrers function of the second kind / rank
 
Normal rank
Property / Symbols used: Ferrers function of the second kind / qualifier
 
test:

𝖰 ν μ ⁡ ( x ) Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

\FerrersQ[\NVar{\mu}]{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Ferrers function of the second kind / qualifier
 
xml-id: C14.S3.E2.m2abdec

Revision as of 00:36, 2 January 2020

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DLMF:14.9.E4
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    Statements

    test
    𝖰 ν - m ⁡ ( x ) = ( - 1 ) m ⁢ Γ ⁡ ( ν - m + 1 ) Γ ⁡ ( ν + m + 1 ) ⁢ 𝖰 ν m ⁡ ( x ) , Ferrers-Legendre-Q-first-kind 𝑚 𝜈 𝑥 superscript 1 𝑚 Euler-Gamma 𝜈 𝑚 1 Euler-Gamma 𝜈 𝑚 1 Ferrers-Legendre-Q-first-kind 𝑚 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}^{-m}_{\nu}\left(x\right)=(-1)^{m}\frac{% \Gamma\left(\nu-m+1\right)}{\Gamma\left(\nu+m+1\right)}\mathsf{Q}^{m}_{\nu}% \left(x\right),}}
    0 references
    DLMF id
    DLMF:14.9.E4
    0 references
    constraint
    ν ≠ m - 1 , m - 2 , … 𝜈 𝑚 1 𝑚 2 … {\displaystyle{\displaystyle\nu\neq m-1,m-2,\dots}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
    Ferrers function of the second kind
    test
    𝖰 ν μ ⁡ ( x ) Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E2.m2abdec
    0 references
     
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