DLMF:14.8.E4 (Q4778): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11591 / rank
 
Normal rank
Property / Symbols used: Q11591 / qualifier
 
test:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11591 / qualifier
 
xml-id: C14.S1.XMD7.m1adec
Property / Symbols used
 
Property / Symbols used: Q11590 / rank
 
Normal rank
Property / Symbols used: Q11590 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11590 / qualifier
 
xml-id: C14.S1.XMD8.m1cdec

Latest revision as of 00:32, 2 January 2020

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DLMF:14.8.E4
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    Statements

    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},}}
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    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}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aadec
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    𝖰 ν μ ( x ) Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    C14.S3.E2.m2adec
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    asymptotically-equals {\displaystyle{\displaystyle\sim}}
    C2.S1.E1.m2abdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
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    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2adec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C14.S1.XMD1.m1cdec
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    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    C14.S1.XMD7.m1adec
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    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C14.S1.XMD8.m1cdec
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