DLMF:14.8.E14 (Q4788): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2ajdec

Revision as of 01:34, 2 January 2020

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DLMF:14.8.E14
No description defined

    Statements

    Defining formula
    P - 1 / 2 μ ⁡ ( x ) ∼ 1 Γ ⁡ ( 1 2 - μ ) ⁢ ( 2 π ⁢ x ) 1 / 2 ⁢ ln ⁡ x , asymptotically-equals Legendre-P-first-kind 𝜇 1 2 𝑥 1 Euler-Gamma 1 2 𝜇 superscript 2 𝜋 𝑥 1 2 𝑥 {\displaystyle{\displaystyle P^{\mu}_{-1/2}\left(x\right)\sim\frac{1}{\Gamma% \left(\frac{1}{2}-\mu\right)}\left(\frac{2}{\pi x}\right)^{1/2}\ln x,}}
    0 references
    DLMF id
    DLMF:14.8.E14
    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
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2ajdec
    0 references
     
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