DLMF:14.12.E2 (Q4823)

From testwiki
Revision as of 00:41, 2 January 2020 by imported>Admin (Admin moved page Main Page to Verifying DLMF with Maple and Mathematica)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:14.12.E2
No description defined

    Statements

    test
    𝖯 ν - μ ⁡ ( x ) = ( 1 - x 2 ) - μ / 2 Γ ⁡ ( μ ) ⁢ ∫ x 1 𝖯 ν ⁡ ( t ) ⁢ ( t - x ) μ - 1 ⁢ d t , Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 superscript 1 superscript 𝑥 2 𝜇 2 Euler-Gamma 𝜇 superscript subscript 𝑥 1 shorthand-Ferrers-Legendre-P-first-kind 𝜈 𝑡 superscript 𝑡 𝑥 𝜇 1 𝑡 {\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{\nu}\left(x\right)=\frac{\left(% 1-x^{2}\right)^{-\mu/2}}{\Gamma\left(\mu\right)}\int_{x}^{1}\mathsf{P}_{\nu}% \left(t\right)(t-x)^{\mu-1}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:14.12.E2
    0 references
    constraint
    ℜ ⁡ μ > 0 𝜇 0 {\displaystyle{\displaystyle\Re\mu>0}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Ferrers function of the first kind
    test
    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.m2aadec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q4823&oldid=26940"