DLMF:14.8.E1 (Q4775): Difference between revisions

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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.m1dec

Latest revision as of 01:31, 2 January 2020

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DLMF:14.8.E1
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    Statements

    Defining formula
    𝖯 ν μ ⁡ ( x ) ∼ 1 Γ ⁡ ( 1 - μ ) ⁢ ( 2 1 - x ) μ / 2 , asymptotically-equals Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 1 Euler-Gamma 1 𝜇 superscript 2 1 𝑥 𝜇 2 {\displaystyle{\displaystyle\mathsf{P}^{\mu}_{\nu}\left(x\right)\sim\frac{1}{% \Gamma\left(1-\mu\right)}\left(\frac{2}{1-x}\right)^{\mu/2},}}
    0 references
    DLMF id
    DLMF:14.8.E1
    0 references
    constraint
    μ ≠ 1 , 2 , 3 , … 𝜇 1 2 3 … {\displaystyle{\displaystyle\mu\neq 1,2,3,\dots}}
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Ferrers function of the first kind
    Defining formula
    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.m2adec
    0 references
    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2adec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1dec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1dec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1dec
    0 references
     
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