DLMF:14.12.E13 (Q4834): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10920 / rank
 
Normal rank
Property / Symbols used: Q10920 / qualifier
 
test:

P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}

\LegendrepolyP{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q10920 / qualifier
 
xml-id: C18.S3.T1.t1.r10.m2aadec
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.m1akdec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5addec
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.m3akdec
Property / Symbols used
 
Property / Symbols used: Q11597 / rank
 
Normal rank
Property / Symbols used: Q11597 / qualifier
 
test:

𝑸 ν ⁡ ( z ) = 𝑸 ν 0 ⁡ ( z ) shorthand-associated-Legendre-black-Q 𝜈 𝑧 associated-Legendre-black-Q 0 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}_{\NVar{\nu}}\left(\NVar{z}\right)=% \boldsymbol{Q}^{0}_{\nu}\left(z\right)}}

\assLegendreOlverQ[]{\NVar{\nu}}@{\NVar{z}}=\assLegendreOlverQ[0]{\nu}@{z}
Property / Symbols used: Q11597 / qualifier
 
xml-id: C14.S2.SS2.p2.m6adec
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.m1jdec
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.m1ddec

Latest revision as of 00:45, 2 January 2020

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DLMF:14.12.E13
No description defined

    Statements

    test
    𝑸 n ⁡ ( x ) = 1 2 ⁢ ( n ! ) ⁢ ∫ - 1 1 P n ⁡ ( t ) x - t ⁢ d t . shorthand-associated-Legendre-black-Q 𝑛 𝑥 1 2 𝑛 superscript subscript 1 1 Legendre-spherical-polynomial 𝑛 𝑡 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle\boldsymbol{Q}_{n}\left(x\right)=\frac{1}{2(n!)}% \int_{-1}^{1}\frac{P_{n}\left(t\right)}{x-t}\mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:14.12.E13
    0 references
    Symbols used
    Q10920
    test
    P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r10.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5addec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
    0 references
    Q11597
    test
    𝑸 ν ⁡ ( z ) = 𝑸 ν 0 ⁡ ( z ) shorthand-associated-Legendre-black-Q 𝜈 𝑧 associated-Legendre-black-Q 0 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}_{\NVar{\nu}}\left(\NVar{z}\right)=% \boldsymbol{Q}^{0}_{\nu}\left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m6adec
    0 references
    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1jdec
    0 references
    Q11602
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1ddec
    0 references
     
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