DLMF:6.5.E4 (Q2244)

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DLMF:6.5.E4
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    Statements

    test
    1 2 ⁢ ( Ei ⁡ ( x ) - E 1 ⁡ ( x ) ) = Chi ⁡ ( x ) = Ci ⁡ ( i ⁢ x ) - 1 2 ⁢ π ⁢ i . 1 2 exponential-integral-Ei 𝑥 exponential-integral 𝑥 hyperbolic-cosine-integral 𝑥 cosine-integral 𝑖 𝑥 1 2 𝜋 𝑖 {\displaystyle{\displaystyle\tfrac{1}{2}(\mathrm{Ei}\left(x\right)-E_{1}\left(% x\right))=\mathrm{Chi}\left(x\right)=\mathrm{Ci}\left(ix\right)-\tfrac{1}{2}% \pi i.}}
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    DLMF id
    DLMF:6.5.E4
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    cosine integral
    test
    Ci ⁡ ( z ) cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E11.m2adec
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    exponential integral
    test
    E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E1.m2acdec
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    Q11306
    test
    Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.SS1.p3.m2acdec
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    hyperbolic cosine integral
    test
    Chi ⁡ ( z ) hyperbolic-cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Chi}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E16.m2adec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
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    Q11307
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C6.S1.XMD1.m1cdec
    0 references
     
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