DLMF:14.28.E2 (Q4961): Difference between revisions

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Property / constraint
 

z 2 ∈ ℰ 2 subscript 𝑧 2 subscript ℰ 2 {\displaystyle{\displaystyle z_{2}\in\mathcal{E}_{2}}}

z_{2}\in\mathcal{E}_{2}
Property / constraint: z 2 ∈ ℰ 2 subscript 𝑧 2 subscript ℰ 2 {\displaystyle{\displaystyle z_{2}\in\mathcal{E}_{2}}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
test:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2adec
Property / Symbols used
 
Property / Symbols used: Q11447 / rank
 
Normal rank
Property / Symbols used: Q11447 / qualifier
 
test:

P ν ⁡ ( z ) = P ν 0 ⁡ ( z ) shorthand-Legendre-P-first-kind 𝜈 𝑧 Legendre-P-first-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}

\assLegendreP[]{\NVar{\nu}}@{\NVar{z}}=\assLegendreP[0]{\nu}@{z}
Property / Symbols used: Q11447 / qualifier
 
xml-id: C14.S2.SS2.p2.m3aadec
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.m5adec
Property / Symbols used
 
Property / Symbols used: Q11638 / rank
 
Normal rank
Property / Symbols used: Q11638 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11638 / qualifier
 
xml-id: C14.S1.XMD4.m1adec
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.m1dec
Property / Symbols used
 
Property / Symbols used: Q11640 / rank
 
Normal rank
Property / Symbols used: Q11640 / qualifier
 
test:

ℰ 1 subscript ℰ 1 {\displaystyle{\displaystyle\mathcal{E}_{1}}}

\mathcal{E}_{1}
Property / Symbols used: Q11640 / qualifier
 
xml-id: C14.S28.XMD1.m1dec

Latest revision as of 13:42, 2 January 2020

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English
DLMF:14.28.E2
No description defined

    Statements

    test
    ∑ n = 0 ∞ ( 2 ⁢ n + 1 ) ⁢ Q n ⁡ ( z 1 ) ⁢ P n ⁡ ( z 2 ) = 1 z 1 - z 2 , superscript subscript 𝑛 0 2 𝑛 1 shorthand-Legendre-Q-second-kind 𝑛 subscript 𝑧 1 shorthand-Legendre-P-first-kind 𝑛 subscript 𝑧 2 1 subscript 𝑧 1 subscript 𝑧 2 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}(2n+1)Q_{n}\left(z_{1}\right)P_% {n}\left(z_{2}\right)=\frac{1}{z_{1}-z_{2}},}}
    0 references
    DLMF id
    DLMF:14.28.E2
    0 references
    constraint
    z 2 ∈ ℰ 2 subscript 𝑧 2 subscript ℰ 2 {\displaystyle{\displaystyle z_{2}\in\mathcal{E}_{2}}}
    0 references
    Symbols used
    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
    0 references
    Q11447
    test
    P ν ⁡ ( z ) = P ν 0 ⁡ ( z ) shorthand-Legendre-P-first-kind 𝜈 𝑧 Legendre-P-first-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m3aadec
    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.m5adec
    0 references
    Q11638
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C14.S1.XMD4.m1adec
    0 references
    Q11602
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1dec
    0 references
    Q11640
    test
    ℰ 1 subscript ℰ 1 {\displaystyle{\displaystyle\mathcal{E}_{1}}}
    xml-id
    C14.S28.XMD1.m1dec
    0 references
     
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