DLMF:4.35.E33 (Q1907)

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DLMF:4.35.E33
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    Statements

    Defining formula
    cosh ⁡ ( n ⁢ z ) ± sinh ⁡ ( n ⁢ z ) = ( cosh ⁡ z ± sinh ⁡ z ) n , plus-or-minus 𝑛 𝑧 𝑛 𝑧 superscript plus-or-minus 𝑧 𝑧 𝑛 {\displaystyle{\displaystyle\cosh\left(nz\right)\pm\sinh\left(nz\right)=(\cosh z% \pm\sinh z)^{n},}}
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    DLMF id
    DLMF:4.35.E33
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    constraint
    n ∈ ℤ 𝑛 {\displaystyle{\displaystyle n\in\mathbb{Z}}}
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    Symbols used
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
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    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2avdec
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    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2audec
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    Q10818
    Defining formula
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2adec
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    Q11223
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1dec
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    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1pdec
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