DLMF:3.4.E17 (Q1221): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
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.m3adec
Property / Symbols used
 
Property / Symbols used: Q11164 / rank
 
Normal rank
Property / Symbols used: Q11164 / qualifier
 
Defining formula:

C 𝐶 {\displaystyle{\displaystyle C}}

C
Property / Symbols used: Q11164 / qualifier
 
xml-id: C3.S4.XMD3.m1dec

Latest revision as of 17:47, 1 January 2020

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English
DLMF:3.4.E17
No description defined

    Statements

    1 k ! f ( k ) ( x 0 ) = 1 2 π i C f ( ζ ) ( ζ - x 0 ) k + 1 d ζ , 1 𝑘 superscript 𝑓 𝑘 subscript 𝑥 0 1 2 𝑖 subscript 𝐶 𝑓 𝜁 superscript 𝜁 subscript 𝑥 0 𝑘 1 𝜁 {\displaystyle{\displaystyle\frac{1}{k!}\,f^{(k)}(x_{0})=\frac{1}{2\pi i}\int_% {C}\frac{f(\zeta)}{(\zeta-x_{0})^{k+1}}\,\mathrm{d}\zeta,}}
    0 references
    DLMF:3.4.E17
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1adec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2adec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3adec
    0 references
    C 𝐶 {\displaystyle{\displaystyle C}}
    C3.S4.XMD3.m1dec
    0 references