DLMF:4.21.E38 (Q1742)

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DLMF:4.21.E38
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    Statements

    Defining formula
    cos ⁡ z = cos ⁡ x ⁢ cosh ⁡ y - i ⁢ sin ⁡ x ⁢ sinh ⁡ y , 𝑧 𝑥 𝑦 imaginary-unit 𝑥 𝑦 {\displaystyle{\displaystyle\cos z=\cos x\cosh y-\mathrm{i}\sin x\sinh y,}}
    0 references
    DLMF id
    DLMF:4.21.E38
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2azdec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2aadec
    0 references
    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aydec
    0 references
    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1adec
    0 references
     
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