DLMF:14.2.E8 (Q4686)

From DRMF
Revision as of 01:11, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:14.2.E8
No description defined

    Statements

    Defining formula
    𝒲 ⁡ { P ν - μ ⁡ ( x ) , 𝑸 ν μ ⁡ ( x ) } = - 1 Γ ⁡ ( ν + μ + 1 ) ⁢ ( x 2 - 1 ) , Wronskian Legendre-P-first-kind 𝜇 𝜈 𝑥 associated-Legendre-black-Q 𝜇 𝜈 𝑥 1 Euler-Gamma 𝜈 𝜇 1 superscript 𝑥 2 1 {\displaystyle{\displaystyle\mathscr{W}\left\{P^{-\mu}_{\nu}\left(x\right),% \boldsymbol{Q}^{\mu}_{\nu}\left(x\right)\right\}=-\frac{1}{\Gamma\left(\nu+\mu% +1\right)\left(x^{2}-1\right)},}}
    0 references
    DLMF id
    DLMF:14.2.E8
    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
    Q11481
    Defining formula
    P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m1aadec
    0 references
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3addec
    0 references
    Q11592
    Defining formula
    𝑸 ν μ ⁡ ( z ) associated-Legendre-black-Q 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m3adec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1gdec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1fdec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1gdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4686&oldid=29827"