DLMF:10.71.E2 (Q3903): Difference between revisions

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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.m1adec
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.m1adec
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.m1adec

Latest revision as of 14:33, 2 January 2020

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DLMF:10.71.E2
No description defined

    Statements

    Defining formula
    ∫ x 1 - ν ⁢ f ν ⁢ d x = x 1 - ν 2 ⁢ ( f ν - 1 - g ν - 1 ) = x 1 - ν ⁢ ( ν x ⁢ g ν + g ν ′ ) . superscript 𝑥 1 𝜈 subscript 𝑓 𝜈 𝑥 superscript 𝑥 1 𝜈 2 subscript 𝑓 𝜈 1 subscript 𝑔 𝜈 1 superscript 𝑥 1 𝜈 𝜈 𝑥 subscript 𝑔 𝜈 superscript subscript 𝑔 𝜈 ′ {\displaystyle{\displaystyle\int x^{1-\nu}f_{\nu}\mathrm{d}x=\frac{x^{1-\nu}}{% \sqrt{2}}(f_{\nu-1}-g_{\nu-1})=x^{1-\nu}\left(\frac{\nu}{x}g_{\nu}+g_{\nu}^{% \prime}\right).}}
    0 references
    DLMF id
    DLMF:10.71.E2
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1adec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1adec
    0 references
    Q11487
    Defining formula
    f ν subscript 𝑓 𝜈 {\displaystyle{\displaystyle f_{\nu}}}
    xml-id
    C10.S63.XMD1.m1adec
    0 references
    Q11488
    Defining formula
    g ν subscript 𝑔 𝜈 {\displaystyle{\displaystyle g_{\nu}}}
    xml-id
    C10.S63.XMD2.m1adec
    0 references
     
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