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DLMF:6.14.E7 - MaRDI portal

DLMF:6.14.E7 (Q3003)

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DLMF:6.14.E7
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    Statements

    DLMF defining formula
    ∫ 0 ∞ Ci ⁡ ( t ) ⁢ si ⁡ ( t ) ⁢ d t = ln ⁡ 2 . superscript subscript 0 cosine-integral 𝑡 shifted-sine-integral 𝑡 𝑡 2 {\displaystyle{\displaystyle\int_{0}^{\infty}\mathrm{Ci}\left(t\right)\mathrm{% si}\left(t\right)\mathrm{d}t=\ln 2.}}
    0 references
    Symbols used
    cosine integral
    DLMF defining formula
    Ci ⁡ ( z ) cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E11.m2acdec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
    0 references
    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    sine integral
    DLMF defining formula
    si ⁡ ( z ) shifted-sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{si}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E10.m2acdec
    0 references

    Identifiers

     
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