DLMF:4.36.E2 (Q1916)

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DLMF:4.36.E2
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    Statements

    Defining formula
    cosh ⁡ z = ∏ n = 1 ∞ ( 1 + 4 ⁢ z 2 ( 2 ⁢ n - 1 ) 2 ⁢ π 2 ) . 𝑧 superscript subscript product 𝑛 1 1 4 superscript 𝑧 2 superscript 2 𝑛 1 2 superscript 𝜋 2 {\displaystyle{\displaystyle\cosh z=\prod_{n=1}^{\infty}\left(1+\frac{4z^{2}}{% (2n-1)^{2}\pi^{2}}\right).}}
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    DLMF id
    DLMF:4.36.E2
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2adec
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    Q11223
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1adec
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