DLMF:6.9.E1 (Q2273)

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DLMF:6.9.E1
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    Statements

    Defining formula
    E 1 ⁡ ( z ) = e - z z + 1 1 + 1 z + 2 1 + 2 z + 3 1 + 3 z + ⁢ ⋯ , exponential-integral 𝑧 continued-fraction superscript 𝑒 𝑧 𝑧 continued-fraction 1 1 continued-fraction 1 𝑧 continued-fraction 2 1 continued-fraction 2 𝑧 continued-fraction 3 1 continued-fraction 3 limit-from 𝑧 ⋯ {\displaystyle{\displaystyle E_{1}\left(z\right)=\cfrac{e^{-z}}{z+\cfrac{1}{1+% \cfrac{1}{z+\cfrac{2}{1+\cfrac{2}{z+\cfrac{3}{1+\cfrac{3}{z+}}}}}}}\cdots,}}
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    DLMF id
    DLMF:6.9.E1
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    constraint
    | ph ⁡ z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}
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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.m2adec
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