DLMF:14.17.E1 (Q4882): Difference between revisions

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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.m1dec

Latest revision as of 13:21, 2 January 2020

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DLMF:14.17.E1
No description defined

    Statements

    Defining formula
    ∫ ( 1 - x 2 ) - μ / 2 ⁢ 𝖯 ν μ ⁡ ( x ) ⁢ d x = - ( 1 - x 2 ) - ( μ - 1 ) / 2 ⁢ 𝖯 ν μ - 1 ⁡ ( x ) . superscript 1 superscript 𝑥 2 𝜇 2 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 𝑥 superscript 1 superscript 𝑥 2 𝜇 1 2 Ferrers-Legendre-P-first-kind 𝜇 1 𝜈 𝑥 {\displaystyle{\displaystyle{\int\left(1-x^{2}\right)^{-\mu/2}\mathsf{P}^{\mu}% _{\nu}\left(x\right)\mathrm{d}x}={-\left(1-x^{2}\right)^{-(\mu-1)/2}\mathsf{P}% ^{\mu-1}_{\nu}\left(x\right)}.}}
    0 references
    DLMF id
    DLMF:14.17.E1
    0 references
    Symbols used
    Ferrers function of the first kind
    Defining formula
    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.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1dec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1dec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1dec
    0 references
     
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