DLMF:6.4.E6 (Q2239): Difference between revisions

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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
 
Defining formula:

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.m2addec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2addec
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.m2addec
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
 
Defining formula:

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: Q11305 / rank
 
Normal rank
Property / Symbols used: Q11305 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11305 / qualifier
 
xml-id: C6.S1.XMD2.m1edec

Latest revision as of 01:23, 2 January 2020

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DLMF:6.4.E6
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    Statements

    f ( z e ± π i ) = π e i z - f ( z ) , sine-cosine-integral-f 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 𝜋 superscript 𝑒 minus-or-plus 𝑖 𝑧 sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(ze^{\pm\pi i}\right)=\pi e^{\mp iz% }-\mathrm{f}\left(z\right),}}
    0 references
    DLMF:6.4.E6
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2addec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2addec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2addec
    0 references
    f ( z ) sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    C6.S2.E17.m2adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C6.S1.XMD2.m1edec
    0 references