DLMF:3.3.E6 (Q1111): 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.m1adec
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: nodal polynomial (locally) / rank
 
Normal rank
Property / Symbols used: nodal polynomial (locally) / qualifier
 
Defining formula:

ω n + 1 ⁢ ( z ) subscript 𝜔 𝑛 1 𝑧 {\displaystyle{\displaystyle\omega_{n+1}(z)}}

\omega_{n+1}(z)
Property / Symbols used: nodal polynomial (locally) / qualifier
 
xml-id: C3.S3.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: remainder (locally) / rank
 
Normal rank
Property / Symbols used: remainder (locally) / qualifier
 
Defining formula:

R n ⁢ ( x ) subscript 𝑅 𝑛 𝑥 {\displaystyle{\displaystyle R_{n}(x)}}

R_{n}(x)
Property / Symbols used: remainder (locally) / qualifier
 
xml-id: C3.S3.XMD4.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11161 / rank
 
Normal rank
Property / Symbols used: Q11161 / qualifier
 
Defining formula:

C 𝐶 {\displaystyle{\displaystyle C}}

C
Property / Symbols used: Q11161 / qualifier
 
xml-id: C3.S3.XMD6.m1dec

Latest revision as of 17:44, 1 January 2020

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DLMF:3.3.E6
No description defined

    Statements

    Defining formula
    R n ⁢ ( z ) = ω n + 1 ⁢ ( z ) 2 ⁢ π ⁢ i ⁢ ∫ C f ⁢ ( ζ ) ( ζ - z ) ⁢ ω n + 1 ⁢ ( ζ ) ⁢ d ζ , subscript 𝑅 𝑛 𝑧 subscript 𝜔 𝑛 1 𝑧 2 imaginary-unit subscript 𝐶 𝑓 𝜁 𝜁 𝑧 subscript 𝜔 𝑛 1 𝜁 𝜁 {\displaystyle{\displaystyle R_{n}(z)=\frac{\omega_{n+1}(z)}{2\pi\mathrm{i}}% \int_{C}\frac{f(\zeta)}{(\zeta-z)\omega_{n+1}(\zeta)}\mathrm{d}\zeta,}}
    0 references
    DLMF id
    DLMF:3.3.E6
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    nodal polynomial (locally)
    Defining formula
    ω n + 1 ⁢ ( z ) subscript 𝜔 𝑛 1 𝑧 {\displaystyle{\displaystyle\omega_{n+1}(z)}}
    xml-id
    C3.S3.XMD2.m1cdec
    0 references
    remainder (locally)
    Defining formula
    R n ⁢ ( x ) subscript 𝑅 𝑛 𝑥 {\displaystyle{\displaystyle R_{n}(x)}}
    xml-id
    C3.S3.XMD4.m1bdec
    0 references
    Q11161
    Defining formula
    C 𝐶 {\displaystyle{\displaystyle C}}
    xml-id
    C3.S3.XMD6.m1dec
    0 references
     
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