DLMF:6.10.E1 (Q2274)

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DLMF:6.10.E1
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    Statements

    Defining formula
    E 1 ⁡ ( z ) = e - z ⁢ ( c 0 z + c 1 z ⁢ ( z + 1 ) + 2 ! ⁢ c 2 z ⁢ ( z + 1 ) ⁢ ( z + 2 ) + 3 ! ⁢ c 3 z ⁢ ( z + 1 ) ⁢ ( z + 2 ) ⁢ ( z + 3 ) + ⋯ ) , exponential-integral 𝑧 superscript 𝑒 𝑧 subscript 𝑐 0 𝑧 subscript 𝑐 1 𝑧 𝑧 1 2 subscript 𝑐 2 𝑧 𝑧 1 𝑧 2 3 subscript 𝑐 3 𝑧 𝑧 1 𝑧 2 𝑧 3 ⋯ {\displaystyle{\displaystyle E_{1}\left(z\right)=e^{-z}\left(\frac{c_{0}}{z}+% \frac{c_{1}}{z(z+1)}+\frac{2!c_{2}}{z(z+1)(z+2)}+\frac{3!c_{3}}{z(z+1)(z+2)(z+% 3)}+\cdots\right),}}
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    DLMF id
    DLMF:6.10.E1
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    constraint
    ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
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    Symbols used
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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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.m2adec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
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