DLMF:6.5.E5 (Q2245)

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DLMF:6.5.E5
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    Statements

    Defining formula
    Si ⁡ ( z ) = 1 2 ⁢ i ⁢ ( E 1 ⁡ ( - i ⁢ z ) - E 1 ⁡ ( i ⁢ z ) ) + 1 2 ⁢ π , sine-integral 𝑧 1 2 𝑖 exponential-integral 𝑖 𝑧 exponential-integral 𝑖 𝑧 1 2 𝜋 {\displaystyle{\displaystyle\mathrm{Si}\left(z\right)=\tfrac{1}{2}i(E_{1}\left% (-iz\right)-E_{1}\left(iz\right))+\tfrac{1}{2}\pi,}}
    0 references
    DLMF id
    DLMF:6.5.E5
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    exponential integral
    Defining formula
    E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E1.m2addec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
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    sine integral
    Defining formula
    Si ⁡ ( z ) sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E9.m2aadec
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    Q11305
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1dec
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