DLMF:14.10.E1 (Q4810): 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 01:38, 2 January 2020

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DLMF:14.10.E1
No description defined

    Statements

    Defining formula
    𝖯 ν μ + 2 ⁡ ( x ) + 2 ⁢ ( μ + 1 ) ⁢ x ⁢ ( 1 - x 2 ) - 1 / 2 ⁢ 𝖯 ν μ + 1 ⁡ ( x ) + ( ν - μ ) ⁢ ( ν + μ + 1 ) ⁢ 𝖯 ν μ ⁡ ( x ) = 0 , Ferrers-Legendre-P-first-kind 𝜇 2 𝜈 𝑥 2 𝜇 1 𝑥 superscript 1 superscript 𝑥 2 1 2 Ferrers-Legendre-P-first-kind 𝜇 1 𝜈 𝑥 𝜈 𝜇 𝜈 𝜇 1 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 0 {\displaystyle{\displaystyle{\mathsf{P}^{\mu+2}_{\nu}\left(x\right)+2(\mu+1)x% \left(1-x^{2}\right)^{-1/2}\mathsf{P}^{\mu+1}_{\nu}\left(x\right)}+(\nu-\mu)(% \nu+\mu+1)\mathsf{P}^{\mu}_{\nu}\left(x\right)=0,}}
    0 references
    DLMF id
    DLMF:14.10.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
    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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