DLMF:14.28.E2 (Q4961)

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DLMF:14.28.E2
No description defined

    Statements

    Defining formula
    ∑ 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}},}}
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    DLMF id
    DLMF:14.28.E2
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    constraint
    z 2 ∈ ℰ 2 subscript 𝑧 2 subscript ℰ 2 {\displaystyle{\displaystyle z_{2}\in\mathcal{E}_{2}}}
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    Symbols used
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
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    Q11447
    Defining formula
    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
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    Q11448
    Defining formula
    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
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    Q11638
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C14.S1.XMD4.m1adec
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    Q11602
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1dec
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    Q11640
    Defining formula
    ℰ 1 subscript ℰ 1 {\displaystyle{\displaystyle\mathcal{E}_{1}}}
    xml-id
    C14.S28.XMD1.m1dec
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