DLMF:10.71.E5 (Q3906): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1addec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3addec
Property / Symbols used
 
Property / Symbols used: Q11435 / rank
 
Normal rank
Property / Symbols used: Q11435 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11435 / qualifier
 
xml-id: C10.S1.XMD4.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11487 / rank
 
Normal rank
Property / Symbols used: Q11487 / qualifier
 
Defining formula:

f ν subscript 𝑓 𝜈 {\displaystyle{\displaystyle f_{\nu}}}

f_{\nu}
Property / Symbols used: Q11487 / qualifier
 
xml-id: C10.S63.XMD1.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11488 / rank
 
Normal rank
Property / Symbols used: Q11488 / qualifier
 
Defining formula:

g ν subscript 𝑔 𝜈 {\displaystyle{\displaystyle g_{\nu}}}

g_{\nu}
Property / Symbols used: Q11488 / qualifier
 
xml-id: C10.S63.XMD2.m1ddec

Latest revision as of 14:33, 2 January 2020

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DLMF:10.71.E5
No description defined

    Statements

    Defining formula
    ∫ x ⁢ ( f ν 2 + g ν 2 ) ⁢ d x = x ⁢ ( f ν ⁢ g ν ′ - f ν ′ ⁢ g ν ) = - x 2 ⁢ ( f ν ⁢ f ν + 1 + g ν ⁢ g ν + 1 - f ν ⁢ g ν + 1 + f ν + 1 ⁢ g ν ) , 𝑥 superscript subscript 𝑓 𝜈 2 superscript subscript 𝑔 𝜈 2 𝑥 𝑥 subscript 𝑓 𝜈 superscript subscript 𝑔 𝜈 ′ superscript subscript 𝑓 𝜈 ′ subscript 𝑔 𝜈 𝑥 2 subscript 𝑓 𝜈 subscript 𝑓 𝜈 1 subscript 𝑔 𝜈 subscript 𝑔 𝜈 1 subscript 𝑓 𝜈 subscript 𝑔 𝜈 1 subscript 𝑓 𝜈 1 subscript 𝑔 𝜈 {\displaystyle{\displaystyle\int x(f_{\nu}^{2}+g_{\nu}^{2})\mathrm{d}x=x(f_{% \nu}g_{\nu}^{\prime}-f_{\nu}^{\prime}g_{\nu})=-\frac{x}{\sqrt{2}}(f_{\nu}f_{% \nu+1}+g_{\nu}g_{\nu+1}-f_{\nu}g_{\nu+1}+f_{\nu+1}g_{\nu}),}}
    0 references
    DLMF id
    DLMF:10.71.E5
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1ddec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1ddec
    0 references
    Q11487
    Defining formula
    f ν subscript 𝑓 𝜈 {\displaystyle{\displaystyle f_{\nu}}}
    xml-id
    C10.S63.XMD1.m1ddec
    0 references
    Q11488
    Defining formula
    g ν subscript 𝑔 𝜈 {\displaystyle{\displaystyle g_{\nu}}}
    xml-id
    C10.S63.XMD2.m1ddec
    0 references
     
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