DLMF:4.4.E12 (Q1546)

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DLMF:4.4.E12
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    Statements

    Defining formula
    i ± i = e ∓ π / 2 . imaginary-unit plus-or-minus imaginary-unit superscript 𝑒 minus-or-plus 𝜋 2 {\displaystyle{\displaystyle{\mathrm{i}^{\pm\mathrm{i}}}=e^{\mp\pi/2}.}}
    0 references
    DLMF id
    DLMF:4.4.E12
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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.m2aidec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aidec
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