DLMF:4.39.E1 (Q2421)

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DLMF:4.39.E1
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    Statements

    DLMF defining formula
    tanh ⁡ z = z 1 + z 2 3 + z 2 5 + z 2 7 + ⋯ , 𝑧 continued-fraction 𝑧 1 continued-fraction superscript 𝑧 2 3 continued-fraction superscript 𝑧 2 5 continued-fraction superscript 𝑧 2 7 ⋯ {\displaystyle{\displaystyle\tanh z=\cfrac{z}{1+\cfrac{z^{2}}{3+\cfrac{z^{2}}{% 5+\cfrac{z^{2}}{7+\cdots}}}},}}
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    constraint
    z ≠ ± 1 2 ⁢ π ⁢ i , ± 3 2 ⁢ π ⁢ i , … 𝑧 plus-or-minus 1 2 𝜋 imaginary-unit plus-or-minus 3 2 𝜋 imaginary-unit … {\displaystyle{\displaystyle z\neq\pm\tfrac{1}{2}\pi\mathrm{i},\pm\tfrac{3}{2}% \pi\mathrm{i},\dots}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    hyperbolic tangent function
    DLMF defining formula
    tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    xml-id
    C4.S28.E4.m2adec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1dec
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    Identifiers

     
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