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DLMF:6.4.E6 - MaRDI portal

DLMF:6.4.E6 (Q2937)

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DLMF:6.4.E6
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    Statements

    DLMF defining formula
    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
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
    auxiliary function for sine and cosine integrals
    DLMF defining formula
    f ⁡ ( z ) sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E17.m2adec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1edec
    0 references

    Identifiers

     
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