DLMF:6.4.E7 (Q2240): Difference between revisions

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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.m1fdec

Latest revision as of 01:23, 2 January 2020

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DLMF:6.4.E7
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    Statements

    Defining formula
    g ⁡ ( z ⁢ e ± π ⁢ i ) = ∓ π ⁢ i ⁢ e ∓ i ⁢ z + g ⁡ ( z ) . sine-cosine-integral-g 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 minus-or-plus 𝜋 𝑖 superscript 𝑒 minus-or-plus 𝑖 𝑧 sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(ze^{\pm\pi i}\right)=\mp\pi ie^{% \mp iz}+\mathrm{g}\left(z\right).}}
    0 references
    DLMF id
    DLMF:6.4.E7
    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.m2aedec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aedec
    0 references
    auxiliary function for sine and cosine integrals
    Defining formula
    g ⁡ ( z ) sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E18.m2adec
    0 references
    Q11305
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1fdec
    0 references
     
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