DLMF:18.28.E2 (Q5977): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: DLMF:18.2.E5 / rank
 
Normal rank
Property / Symbols used: DLMF:18.2.E5 / qualifier
 
Defining formula:

h n subscript ℎ 𝑛 {\displaystyle{\displaystyle h_{n}}}

h_{n}
Property / Symbols used: DLMF:18.2.E5 / qualifier
 
xml-id: C18.S2.XMD4.m1dec

Latest revision as of 01:53, 2 January 2020

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DLMF:18.28.E2
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    Statements

    Defining formula
    ∫ - 1 1 p n ⁢ ( x ) ⁢ p m ⁢ ( x ) ⁢ w ⁢ ( x ) ⁢ d x = h n ⁢ δ n , m , superscript subscript 1 1 subscript 𝑝 𝑛 𝑥 subscript 𝑝 𝑚 𝑥 𝑤 𝑥 𝑥 subscript ℎ 𝑛 Kronecker 𝑛 𝑚 {\displaystyle{\displaystyle\int_{-1}^{1}p_{n}(x)p_{m}(x)w(x)\mathrm{d}x=h_{n}% \delta_{n,m},}}
    0 references
    DLMF id
    DLMF:18.28.E2
    0 references
    constraint
    | a | , | b | , | c | , | d | ≤ 1 𝑎 𝑏 𝑐 𝑑 1 {\displaystyle{\displaystyle|a|,|b|,|c|,|d|\leq 1}}
    0 references
    Symbols used
    Q10768
    Defining formula
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11729
    Defining formula
    w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    xml-id
    C18.S1.XMD10.m1dec
    0 references
    Q11730
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1dec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1adec
    0 references
    Q11731
    Defining formula
    p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    xml-id
    C18.S1.XMD9.m1adec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1adec
    0 references
    DLMF:18.2.E5
    Defining formula
    h n subscript ℎ 𝑛 {\displaystyle{\displaystyle h_{n}}}
    xml-id
    C18.S2.XMD4.m1dec
    0 references
     
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