DLMF:14.10.E5 (Q4814): 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.m1ddec

Latest revision as of 01:39, 2 January 2020

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DLMF:14.10.E5
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    Statements

    Defining formula
    ( 1 - x 2 ) ⁢ d 𝖯 ν μ ⁡ ( x ) d x = ( ν + μ ) ⁢ 𝖯 ν - 1 μ ⁡ ( x ) - ν ⁢ x ⁢ 𝖯 ν μ ⁡ ( x ) . 1 superscript 𝑥 2 derivative Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 𝑥 𝜈 𝜇 Ferrers-Legendre-P-first-kind 𝜇 𝜈 1 𝑥 𝜈 𝑥 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\left(1-x^{2}\right)\frac{\mathrm{d}\mathsf{P}^{% \mu}_{\nu}\left(x\right)}{\mathrm{d}x}=(\nu+\mu)\mathsf{P}^{\mu}_{\nu-1}\left(% x\right)-\nu x\mathsf{P}^{\mu}_{\nu}\left(x\right).}}
    0 references
    DLMF id
    DLMF:14.10.E5
    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.m2addec
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2aadec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1ddec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1ddec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1ddec
    0 references
     
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