DLMF:14.8.E4 (Q4778): 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 00:32, 2 January 2020

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DLMF:14.8.E4
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    Statements

    test
    𝖰 ν μ ⁡ ( x ) ∼ 1 2 ⁢ cos ⁡ ( μ ⁢ π ) ⁢ Γ ⁡ ( μ ) ⁢ ( 2 1 - x ) μ / 2 , asymptotically-equals Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 1 2 𝜇 𝜋 Euler-Gamma 𝜇 superscript 2 1 𝑥 𝜇 2 {\displaystyle{\displaystyle\mathsf{Q}^{\mu}_{\nu}\left(x\right)\sim\frac{1}{2% }\cos\left(\mu\pi\right)\Gamma\left(\mu\right)\left(\frac{2}{1-x}\right)^{\mu/% 2},}}
    0 references
    DLMF id
    DLMF:14.8.E4
    0 references
    constraint
    μ ≠ 1 2 , 3 2 , 5 2 , … 𝜇 1 2 3 2 5 2 … {\displaystyle{\displaystyle\mu\neq\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{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.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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