DLMF:14.8.E6 (Q4780)

From DRMF
Revision as of 01:32, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:14.8.E6
No description defined

    Statements

    Defining formula
    𝖰 ν - μ ⁡ ( x ) ∼ Γ ⁡ ( μ ) ⁢ Γ ⁡ ( ν - μ + 1 ) 2 ⁢ Γ ⁡ ( ν + μ + 1 ) ⁢ ( 2 1 - x ) μ / 2 , asymptotically-equals Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 Euler-Gamma 𝜇 Euler-Gamma 𝜈 𝜇 1 2 Euler-Gamma 𝜈 𝜇 1 superscript 2 1 𝑥 𝜇 2 {\displaystyle{\displaystyle\mathsf{Q}^{-\mu}_{\nu}\left(x\right)\sim\frac{% \Gamma\left(\mu\right)\Gamma\left(\nu-\mu+1\right)}{2\Gamma\left(\nu+\mu+1% \right)}\left(\frac{2}{1-x}\right)^{\mu/2},}}
    0 references
    DLMF id
    DLMF:14.8.E6
    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.m2acdec
    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.m2abdec
    0 references
    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2addec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1edec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1cdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4780&oldid=32432"