DLMF:18.2.E13 (Q5506)

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DLMF:18.2.E13
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    Statements

    Defining formula
    ∑ ℓ = 0 n ( p ℓ ⁢ ( x ) ) 2 h ℓ = k n h n ⁢ k n + 1 ⁢ ( p n + 1 ′ ⁢ ( x ) ⁢ p n ⁢ ( x ) - p n ′ ⁢ ( x ) ⁢ p n + 1 ⁢ ( x ) ) . superscript subscript ℓ 0 𝑛 superscript subscript 𝑝 ℓ 𝑥 2 subscript ℎ ℓ subscript 𝑘 𝑛 subscript ℎ 𝑛 subscript 𝑘 𝑛 1 superscript subscript 𝑝 𝑛 1 ′ 𝑥 subscript 𝑝 𝑛 𝑥 superscript subscript 𝑝 𝑛 ′ 𝑥 subscript 𝑝 𝑛 1 𝑥 {\displaystyle{\displaystyle\sum_{\ell=0}^{n}\frac{(p_{\ell}(x))^{2}}{h_{\ell}% }=\frac{k_{n}}{h_{n}k_{n+1}}{\left(p_{n+1}^{\prime}(x)p_{n}(x)-p_{n}^{\prime}(% x)p_{n+1}(x)\right)}.}}
    0 references
    DLMF id
    DLMF:18.2.E13
    0 references
    comment
    Warning: Falling back to standard tex;
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    Symbols used
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1adec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ldec
    0 references
    Q11731
    Defining formula
    p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    xml-id
    C18.S1.XMD9.m1idec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1jdec
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    DLMF:18.2.E5
    Defining formula
    h n subscript ℎ 𝑛 {\displaystyle{\displaystyle h_{n}}}
    xml-id
    C18.S2.XMD4.m1ddec
    0 references
    DLMF:18.2.E7
    Defining formula
    k n subscript 𝑘 𝑛 {\displaystyle{\displaystyle k_{n}}}
    xml-id
    C18.S2.XMD6.m1ddec
    0 references
     
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