DLMF:14.8.E11 (Q4785): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11591 / rank
 
Normal rank
Property / Symbols used: Q11591 / qualifier
 
Defining formula:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11591 / qualifier
 
xml-id: C14.S1.XMD7.m1edec
Property / Symbols used
 
Property / Symbols used: Q11590 / rank
 
Normal rank
Property / Symbols used: Q11590 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11590 / qualifier
 
xml-id: C14.S1.XMD8.m1idec

Latest revision as of 01:34, 2 January 2020

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DLMF:14.8.E11
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    Statements

    Defining formula
    𝑸 ν μ ⁡ ( x ) ∼ Γ ⁡ ( μ ) 2 ⁢ Γ ⁡ ( ν + μ + 1 ) ⁢ ( 2 x - 1 ) μ / 2 , asymptotically-equals associated-Legendre-black-Q 𝜇 𝜈 𝑥 Euler-Gamma 𝜇 2 Euler-Gamma 𝜈 𝜇 1 superscript 2 𝑥 1 𝜇 2 {\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(x\right)\sim\frac{% \Gamma\left(\mu\right)}{2\Gamma\left(\nu+\mu+1\right)}\left(\frac{2}{x-1}% \right)^{\mu/2},}}
    0 references
    DLMF id
    DLMF:14.8.E11
    0 references
    constraint
    ℜ ⁡ μ > 0 𝜇 0 {\displaystyle{\displaystyle\Re\mu>0}}
    0 references
    ℜ ⁡ μ > 0 𝜇 0 {\displaystyle{\displaystyle\Re\mu>0}}
    0 references
    ν + μ ≠ - 1 , - 2 , - 3 , … 𝜈 𝜇 1 2 3 … {\displaystyle{\displaystyle\nu+\mu\neq-1,-2,-3,\dots}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2agdec
    0 references
    Q11592
    Defining formula
    𝑸 ν μ ⁡ ( z ) associated-Legendre-black-Q 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m3adec
    0 references
    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2agdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1jdec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1edec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1idec
    0 references
     
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