DLMF:14.12.E11 (Q4832): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11592 / rank
 
Normal rank
Property / Symbols used: Q11592 / qualifier
 
test:

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

\assLegendreOlverQ[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Q11592 / qualifier
 
xml-id: C14.S21.SS1.p1.m3abdec
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.m1aidec
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.m5abdec
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.m3aidec
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.m1bdec

Latest revision as of 00:44, 2 January 2020

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DLMF:14.12.E11
No description defined

    Statements

    test
    𝑸 n m ⁡ ( x ) = ( x 2 - 1 ) m / 2 2 n + 1 ⁢ n ! ⁢ ∫ - 1 1 ( 1 - t 2 ) n ( x - t ) n + m + 1 ⁢ d t , associated-Legendre-black-Q 𝑚 𝑛 𝑥 superscript superscript 𝑥 2 1 𝑚 2 superscript 2 𝑛 1 𝑛 superscript subscript 1 1 superscript 1 superscript 𝑡 2 𝑛 superscript 𝑥 𝑡 𝑛 𝑚 1 𝑡 {\displaystyle{\displaystyle\boldsymbol{Q}^{m}_{n}\left(x\right)=\frac{\left(x% ^{2}-1\right)^{m/2}}{2^{n+1}n!}\int_{-1}^{1}\frac{\left(1-t^{2}\right)^{n}}{(x% -t)^{n+m+1}}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:14.12.E11
    0 references
    Symbols used
    Q11592
    test
    𝑸 ν μ ⁡ ( z ) associated-Legendre-black-Q 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m3abdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aidec
    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.m1bdec
    0 references
     
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