DLMF:14.8.E5 (Q4779): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1ddec
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.m1bdec
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.m1ddec

Latest revision as of 01:32, 2 January 2020

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DLMF:14.8.E5
No description defined

    Statements

    Defining formula
    𝖰 ν μ ⁡ ( x ) ∼ ( - 1 ) μ + ( 1 / 2 ) ⁢ π ⁢ Γ ⁡ ( ν + μ + 1 ) 2 ⁢ Γ ⁡ ( μ + 1 ) ⁢ Γ ⁡ ( ν - μ + 1 ) ⁢ ( 1 - x 2 ) μ / 2 , asymptotically-equals Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 superscript 1 𝜇 1 2 𝜋 Euler-Gamma 𝜈 𝜇 1 2 Euler-Gamma 𝜇 1 Euler-Gamma 𝜈 𝜇 1 superscript 1 𝑥 2 𝜇 2 {\displaystyle{\displaystyle\mathsf{Q}^{\mu}_{\nu}\left(x\right)\sim(-1)^{\mu+% (1/2)}\frac{\pi\Gamma\left(\nu+\mu+1\right)}{2\Gamma\left(\mu+1\right)\Gamma% \left(\nu-\mu+1\right)}\left(\frac{1-x}{2}\right)^{\mu/2},}}
    0 references
    DLMF id
    DLMF:14.8.E5
    0 references
    constraint
    ν ± μ ≠ - 1 , - 2 , - 3 , … plus-or-minus 𝜈 𝜇 1 2 3 … {\displaystyle{\displaystyle\nu\pm\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.m2abdec
    0 references
    Ferrers function of the second kind
    Defining formula
    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.m2aadec
    0 references
    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1ddec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1bdec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1ddec
    0 references
     
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