DLMF:9.10.E10 (Q2892): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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.m3aidec

Revision as of 14:45, 2 January 2020

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DLMF:9.10.E10
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    Statements

    Defining formula
    ∫ z n + 3 ⁢ w ⁢ ( z ) ⁢ d z = z n + 2 ⁢ w ′ ⁢ ( z ) - ( n + 2 ) ⁢ z n + 1 ⁢ w ⁢ ( z ) + ( n + 1 ) ⁢ ( n + 2 ) ⁢ ∫ z n ⁢ w ⁢ ( z ) ⁢ d z , superscript 𝑧 𝑛 3 𝑤 𝑧 𝑧 superscript 𝑧 𝑛 2 superscript 𝑤 ′ 𝑧 𝑛 2 superscript 𝑧 𝑛 1 𝑤 𝑧 𝑛 1 𝑛 2 superscript 𝑧 𝑛 𝑤 𝑧 𝑧 {\displaystyle{\displaystyle\int z^{n+3}w(z)\mathrm{d}z=z^{n+2}w^{\prime}(z)-(% n+2)z^{n+1}w(z)+(n+1)(n+2)\int z^{n}w(z)\mathrm{d}z,}}
    0 references
    DLMF id
    DLMF:9.10.E10
    0 references
    constraint
    n = 0 , 1 , 2 , … . 𝑛 0 1 2 … {\displaystyle{\displaystyle n=0,1,2,\ldots.}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aidec
    0 references
     
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