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DLMF:8.21.E1 - MaRDI portal

DLMF:8.21.E1 (Q3420)

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DLMF:8.21.E1
No description defined

    Statements

    DLMF defining formula
    ci ⁡ ( a , z ) ± i ⁢ si ⁡ ( a , z ) = e ± 1 2 ⁢ π ⁢ i ⁢ a ⁢ Γ ⁡ ( a , z ⁢ e ∓ 1 2 ⁢ π ⁢ i ) , plus-or-minus generalized-cosine-integral-ci 𝑎 𝑧 𝑖 generalized-sine-integral-si 𝑎 𝑧 superscript 𝑒 plus-or-minus 1 2 𝜋 𝑖 𝑎 incomplete-Gamma 𝑎 𝑧 superscript 𝑒 minus-or-plus 1 2 𝜋 𝑖 {\displaystyle{\displaystyle\mathrm{ci}\left(a,z\right)\pm i\mathrm{si}\left(a% ,z\right)=e^{\pm\frac{1}{2}\pi ia}\Gamma\left(a,ze^{\mp\frac{1}{2}\pi i}\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.m2adec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    incomplete gamma function
    DLMF defining formula
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2adec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1dec
    0 references
    parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1dec
    0 references

    Identifiers

     
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