DLMF:14.7.E7 (Q4759): 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.m2acdec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11448 / rank
 
Normal rank
Property / Symbols used: Q11448 / qualifier
 
test:

Q ν ⁡ ( z ) = Q ν 0 ⁡ ( z ) shorthand-Legendre-Q-second-kind 𝜈 𝑧 Legendre-Q-second-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}% \left(z\right)}}

\assLegendreQ[]{\NVar{\nu}}@{\NVar{z}}=\assLegendreQ[0]{\nu}@{z}
Property / Symbols used: Q11448 / qualifier
 
xml-id: C14.S2.SS2.p2.m5aadec
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.m1fdec
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.m1edec
Property / Symbols used
 
Property / Symbols used: Q11603 / rank
 
Normal rank
Property / Symbols used: Q11603 / qualifier
 
test:

W n - 1 ⁢ ( x ) subscript 𝑊 𝑛 1 𝑥 {\displaystyle{\displaystyle W_{n-1}(x)}}

W_{n-1}(x)
Property / Symbols used: Q11603 / qualifier
 
xml-id: C14.S7.XMD1.m1ddec

Latest revision as of 00:28, 2 January 2020

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DLMF:14.7.E7
No description defined

    Statements

    test
    Q n ⁡ ( x ) = 1 2 ⁢ P n ⁡ ( x ) ⁢ ln ⁡ ( x + 1 x - 1 ) - W n - 1 ⁢ ( x ) , shorthand-Legendre-Q-second-kind 𝑛 𝑥 1 2 Legendre-spherical-polynomial 𝑛 𝑥 𝑥 1 𝑥 1 subscript 𝑊 𝑛 1 𝑥 {\displaystyle{\displaystyle Q_{n}\left(x\right)=\frac{1}{2}P_{n}\left(x\right% )\ln\left(\frac{x+1}{x-1}\right)-W_{n-1}(x),}}
    0 references
    DLMF id
    DLMF:14.7.E7
    0 references
    constraint
    n = 0 , 1 , 2 , … 𝑛 0 1 2 … {\displaystyle{\displaystyle n=0,1,2,\dots}}
    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.m2acdec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q11448
    test
    Q ν ⁡ ( z ) = Q ν 0 ⁡ ( z ) shorthand-Legendre-Q-second-kind 𝜈 𝑧 Legendre-Q-second-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}% \left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m5aadec
    0 references
    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1fdec
    0 references
    Q11602
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1edec
    0 references
    Q11603
    test
    W n - 1 ⁢ ( x ) subscript 𝑊 𝑛 1 𝑥 {\displaystyle{\displaystyle W_{n-1}(x)}}
    xml-id
    C14.S7.XMD1.m1ddec
    0 references
     
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