DLMF:20.2.E10 (Q6750)

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DLMF:20.2.E10
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    Statements

    Defining formula
    M ≡ M ⁢ ( z | τ ) = e i ⁢ z + ( i ⁢ π ⁢ τ / 4 ) , equal-by definition 𝑀 𝑀 conditional 𝑧 𝜏 superscript 𝑒 𝑖 𝑧 𝑖 𝜋 𝜏 4 {\displaystyle{\displaystyle M\equiv M(z|\tau)=e^{iz+(i\pi\tau/4)},}}
    0 references
    DLMF id
    DLMF:20.2.E10
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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.m2aedec
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    Q10769
    Defining formula
    ≡ equal-by definition {\displaystyle{\displaystyle\equiv}}
    xml-id
    introduction.Sx4.p1.t1.r9.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
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    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1jdec
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