DLMF:14.2.E4 (Q4682): 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.m2adec

Revision as of 00:10, 2 January 2020

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DLMF:14.2.E4
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    Statements

    test
    𝒲 ⁡ { 𝖯 ν μ ⁡ ( x ) , 𝖰 ν μ ⁡ ( x ) } = Γ ⁡ ( ν + μ + 1 ) Γ ⁡ ( ν - μ + 1 ) ⁢ ( 1 - x 2 ) , Wronskian Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 Euler-Gamma 𝜈 𝜇 1 Euler-Gamma 𝜈 𝜇 1 1 superscript 𝑥 2 {\displaystyle{\displaystyle\mathscr{W}\left\{\mathsf{P}^{\mu}_{\nu}\left(x% \right),\mathsf{Q}^{\mu}_{\nu}\left(x\right)\right\}=\frac{\Gamma\left(\nu+\mu% +1\right)}{\Gamma\left(\nu-\mu+1\right)\left(1-x^{2}\right)},}}
    0 references
    DLMF id
    DLMF:14.2.E4
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Ferrers function of the first kind
    test
    𝖯 ν μ ⁡ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E1.m2aadec
    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.m2adec
    0 references
     
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