DLMF:4.28.E3 (Q1840)

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DLMF:4.28.E3
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    Statements

    Defining formula
    cosh ⁡ z ± sinh ⁡ z = e ± z , plus-or-minus 𝑧 𝑧 superscript 𝑒 plus-or-minus 𝑧 {\displaystyle{\displaystyle\cosh z\pm\sinh z=e^{\pm z},}}
    0 references
    DLMF id
    DLMF:4.28.E3
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    Symbols used
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2aadec
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    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2aadec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1bdec
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