DLMF:14.10.E4 (Q4813): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Ferrers function of the first kind / rank
 
Normal rank
Property / Symbols used: Ferrers function of the first kind / qualifier
 
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)}}

\FerrersP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Ferrers function of the first kind / qualifier
 
xml-id: C14.S3.E1.m2acdec
Property / Symbols used
 
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
test:

d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

\deriv{\NVar{f}}{\NVar{x}}
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S4.E4.m2adec
Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11591 / rank
 
Normal rank
Property / Symbols used: Q11591 / qualifier
 
test:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11591 / qualifier
 
xml-id: C14.S1.XMD7.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11590 / rank
 
Normal rank
Property / Symbols used: Q11590 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11590 / qualifier
 
xml-id: C14.S1.XMD8.m1cdec

Latest revision as of 00:39, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:14.10.E4
No description defined

    Statements

    test
    ( 1 - x 2 ) ⁢ d 𝖯 ν μ ⁡ ( x ) d x = ( μ - ν - 1 ) ⁢ 𝖯 ν + 1 μ ⁡ ( x ) + ( ν + 1 ) ⁢ x ⁢ 𝖯 ν μ ⁡ ( x ) , 1 superscript 𝑥 2 derivative Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 𝑥 𝜇 𝜈 1 Ferrers-Legendre-P-first-kind 𝜇 𝜈 1 𝑥 𝜈 1 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}={(\mu-\nu-1)\mathsf{P}^{\mu}_{\nu+1}% \left(x\right)+(\nu+1)x\mathsf{P}^{\mu}_{\nu}\left(x\right)},}}
    0 references
    DLMF id
    DLMF:14.10.E4
    0 references
    Symbols used
    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.m2acdec
    0 references
    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2adec
    0 references
    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1cdec
    0 references
    Q11591
    test
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1cdec
    0 references
    Q11590
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1cdec
    0 references
     
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