DLMF:18.2.E1 (Q5490): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11729 / rank
 
Normal rank
Property / Symbols used: Q11729 / qualifier
 
Defining formula:

w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}

w(x)
Property / Symbols used: Q11729 / qualifier
 
xml-id: C18.S1.XMD10.m1dec
Property / Symbols used
 
Property / Symbols used: Q11730 / rank
 
Normal rank
Property / Symbols used: Q11730 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11730 / qualifier
 
xml-id: C18.S1.XMD5.m1dec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q11731 / rank
 
Normal rank
Property / Symbols used: Q11731 / qualifier
 
Defining formula:

p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}

p_{n}(x)
Property / Symbols used: Q11731 / qualifier
 
xml-id: C18.S1.XMD9.m1dec
Property / Symbols used
 
Property / Symbols used: Q11732 / rank
 
Normal rank
Property / Symbols used: Q11732 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11732 / qualifier
 
xml-id: C18.S2.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q11733 / rank
 
Normal rank
Property / Symbols used: Q11733 / qualifier
 
Defining formula:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q11733 / qualifier
 
xml-id: C18.S2.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1dec

Latest revision as of 15:13, 2 January 2020

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DLMF:18.2.E1
No description defined

    Statements

    Defining formula
    ∫ a b p n ⁢ ( x ) ⁢ p m ⁢ ( x ) ⁢ w ⁢ ( x ) ⁢ d x = 0 , superscript subscript 𝑎 𝑏 subscript 𝑝 𝑛 𝑥 subscript 𝑝 𝑚 𝑥 𝑤 𝑥 𝑥 0 {\displaystyle{\displaystyle\int_{a}^{b}p_{n}(x)p_{m}(x)w(x)\mathrm{d}x=0,}}
    0 references
    DLMF id
    DLMF:18.2.E1
    0 references
    constraint
    n ≠ m 𝑛 𝑚 {\displaystyle{\displaystyle n\neq m}}
    0 references
    Symbols used
    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.m1dec
    0 references
    Q11731
    Defining formula
    p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    xml-id
    C18.S1.XMD9.m1dec
    0 references
    Q11732
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C18.S2.XMD1.m1dec
    0 references
    Q11733
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C18.S2.XMD2.m1dec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1dec
    0 references
     
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