DLMF:2.5.E36 (Q812): Difference between revisions

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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.m2agdec
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.m3ahdec
Property / Symbols used
 
Property / Symbols used: order less than / rank
 
Normal rank
Property / Symbols used: order less than / qualifier
 
Defining formula:

o ⁡ ( x ) little-o 𝑥 {\displaystyle{\displaystyle o\left(\NVar{x}\right)}}

\littleo@{\NVar{x}}
Property / Symbols used: order less than / qualifier
 
xml-id: C2.S1.E2.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11010 / rank
 
Normal rank
Property / Symbols used: Q11010 / qualifier
 
Defining formula:

G j ⁢ k ⁢ ( z ) subscript 𝐺 𝑗 𝑘 𝑧 {\displaystyle{\displaystyle G_{jk}(z)}}

G_{jk}(z)
Property / Symbols used: Q11010 / qualifier
 
xml-id: C2.S5.XMD21.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11012 / rank
 
Normal rank
Property / Symbols used: Q11012 / qualifier
 
Defining formula:

q j ⁢ k > p j ⁢ k subscript 𝑞 𝑗 𝑘 subscript 𝑝 𝑗 𝑘 {\displaystyle{\displaystyle q_{jk}>p_{jk}}}

q_{jk}>p_{jk}
Property / Symbols used: Q11012 / qualifier
 
xml-id: C2.S5.XMD23.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11013 / rank
 
Normal rank
Property / Symbols used: Q11013 / qualifier
 
Defining formula:

E j ⁢ k ⁢ ( x ) subscript 𝐸 𝑗 𝑘 𝑥 {\displaystyle{\displaystyle E_{jk}(x)}}

E_{jk}(x)
Property / Symbols used: Q11013 / qualifier
 
xml-id: C2.S5.XMD24.m1adec

Latest revision as of 17:06, 1 January 2020

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DLMF:2.5.E36
No description defined

    Statements

    Defining formula
    E j ⁢ k ⁢ ( x ) = 1 2 ⁢ π ⁢ i ⁢ ∫ q j ⁢ k - i ⁢ ∞ q j ⁢ k + i ⁢ ∞ x - z ⁢ G j ⁢ k ⁢ ( z ) ⁢ d z = o ⁡ ( x - q j ⁢ k ) subscript 𝐸 𝑗 𝑘 𝑥 1 2 𝜋 𝑖 superscript subscript subscript 𝑞 𝑗 𝑘 𝑖 subscript 𝑞 𝑗 𝑘 𝑖 superscript 𝑥 𝑧 subscript 𝐺 𝑗 𝑘 𝑧 𝑧 little-o superscript 𝑥 subscript 𝑞 𝑗 𝑘 {\displaystyle{\displaystyle E_{jk}(x)=\frac{1}{2\pi i}\int_{q_{jk}-i\infty}^{% q_{jk}+i\infty}x^{-z}G_{jk}(z)\mathrm{d}z=o\left(x^{-q_{jk}}\right)}}
    0 references
    DLMF id
    DLMF:2.5.E36
    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.m2agdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2agdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
    0 references
    order less than
    Defining formula
    o ⁡ ( x ) little-o 𝑥 {\displaystyle{\displaystyle o\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E2.m2aadec
    0 references
    Q11010
    Defining formula
    G j ⁢ k ⁢ ( z ) subscript 𝐺 𝑗 𝑘 𝑧 {\displaystyle{\displaystyle G_{jk}(z)}}
    xml-id
    C2.S5.XMD21.m1ddec
    0 references
    Q11012
    Defining formula
    q j ⁢ k > p j ⁢ k subscript 𝑞 𝑗 𝑘 subscript 𝑝 𝑗 𝑘 {\displaystyle{\displaystyle q_{jk}>p_{jk}}}
    xml-id
    C2.S5.XMD23.m1bdec
    0 references
    Q11013
    Defining formula
    E j ⁢ k ⁢ ( x ) subscript 𝐸 𝑗 𝑘 𝑥 {\displaystyle{\displaystyle E_{jk}(x)}}
    xml-id
    C2.S5.XMD24.m1adec
    0 references
     
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