DLMF:14.17.E9 (Q4890): 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.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q10768 / rank
 
Normal rank
Property / Symbols used: Q10768 / qualifier
 
test:

δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}

\Kroneckerdelta{\NVar{j}}{\NVar{k}}
Property / Symbols used: Q10768 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r4.m5acdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1ahdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3ahdec
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.m1hdec
Property / Symbols used
 
Property / Symbols used: Q11593 / rank
 
Normal rank
Property / Symbols used: Q11593 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11593 / qualifier
 
xml-id: C14.S1.XMD5.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11602 / rank
 
Normal rank
Property / Symbols used: Q11602 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11602 / qualifier
 
xml-id: C14.S1.XMD6.m1cdec

Latest revision as of 12:23, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:14.17.E9
No description defined

    Statements

    test
    ∫ - 1 1 𝖯 n l ⁡ ( x ) ⁢ 𝖯 n - m ⁡ ( x ) 1 - x 2 ⁢ d x = ( - 1 ) l l ⁢ δ l , m , superscript subscript 1 1 Ferrers-Legendre-P-first-kind 𝑙 𝑛 𝑥 Ferrers-Legendre-P-first-kind 𝑚 𝑛 𝑥 1 superscript 𝑥 2 𝑥 superscript 1 𝑙 𝑙 Kronecker 𝑙 𝑚 {\displaystyle{\displaystyle\int_{-1}^{1}\frac{\mathsf{P}^{l}_{n}\left(x\right% )\mathsf{P}^{-m}_{n}\left(x\right)}{1-x^{2}}\mathrm{d}x=\frac{(-1)^{l}}{l}% \delta_{l,m},}}
    0 references
    DLMF id
    DLMF:14.17.E9
    0 references
    constraint
    l > 0 𝑙 0 {\displaystyle{\displaystyle l>0}}
    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.m2ahdec
    0 references
    Q10768
    test
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5acdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
    0 references
    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1hdec
    0 references
    Q11593
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1cdec
    0 references
    Q11602
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1cdec
    0 references
     
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