DLMF:4.35.E27 (Q1901)

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DLMF:4.35.E27
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    Statements

    Defining formula
    cosh ⁡ ( 2 ⁢ z ) = 2 ⁢ cosh 2 ⁡ z - 1 = 2 ⁢ sinh 2 ⁡ z + 1 = cosh 2 ⁡ z + sinh 2 ⁡ z , 2 𝑧 2 2 𝑧 1 2 2 𝑧 1 2 𝑧 2 𝑧 {\displaystyle{\displaystyle\cosh\left(2z\right)=2{\cosh^{2}}z-1=2{\sinh^{2}}z% +1\\ ={\cosh^{2}}z+{\sinh^{2}}z,}}
    0 references
    DLMF id
    DLMF:4.35.E27
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    Symbols used
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2ardec
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    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2aqdec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1jdec
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