DLMF:6.7.E12 (Q2265): Difference between revisions

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Property / constraint
 

| ph ⁡ z | ≤ π . phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi.}}

|\phase@@{z}|\leq\pi.
Property / constraint: | ph ⁡ z | ≤ π . phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi.}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1akdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2akdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

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

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3akdec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
test:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1adec
Property / Symbols used
 
Property / Symbols used: auxiliary function for sine and cosine integrals / rank
 
Normal rank
Property / Symbols used: auxiliary function for sine and cosine integrals / qualifier
 
test:

f ⁡ ( z ) sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}

\auxsincosintf@{\NVar{z}}
Property / Symbols used: auxiliary function for sine and cosine integrals / qualifier
 
xml-id: C6.S2.E17.m2adec
Property / Symbols used
 
Property / Symbols used: auxiliary function for sine and cosine integrals / rank
 
Normal rank
Property / Symbols used: auxiliary function for sine and cosine integrals / qualifier
 
test:

g ⁡ ( z ) sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}

\auxsincosintg@{\NVar{z}}
Property / Symbols used: auxiliary function for sine and cosine integrals / qualifier
 
xml-id: C6.S2.E18.m2adec
Property / Symbols used
 
Property / Symbols used: Q11305 / rank
 
Normal rank
Property / Symbols used: Q11305 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11305 / qualifier
 
xml-id: C6.S1.XMD2.m1bdec

Latest revision as of 00:29, 2 January 2020

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DLMF:6.7.E12
No description defined

    Statements

    test
    g ⁡ ( z ) + i ⁢ f ⁡ ( z ) = e - i ⁢ z ⁢ ∫ z ∞ e i ⁢ t t ⁢ d t , sine-cosine-integral-g 𝑧 𝑖 sine-cosine-integral-f 𝑧 superscript 𝑒 𝑖 𝑧 superscript subscript 𝑧 superscript 𝑒 𝑖 𝑡 𝑡 𝑡 {\displaystyle{\displaystyle\mathrm{g}\left(z\right)+i\mathrm{f}\left(z\right)% =e^{-iz}\int_{z}^{\infty}\frac{e^{it}}{t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:6.7.E12
    0 references
    constraint
    | ph ⁡ z | ≤ π . phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi.}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2akdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    auxiliary function for sine and cosine integrals
    test
    f ⁡ ( z ) sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E17.m2adec
    0 references
    auxiliary function for sine and cosine integrals
    test
    g ⁡ ( z ) sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E18.m2adec
    0 references
    Q11305
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1bdec
    0 references
     
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