DLMF:10.32.E12 (Q3532)

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DLMF:10.32.E12
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    Statements

    Defining formula
    I ν ⁡ ( z ) = 1 2 ⁢ π ⁢ i ⁢ ∫ ∞ - i ⁢ π ∞ + i ⁢ π e z ⁢ cosh ⁡ t - ν ⁢ t ⁢ d t , modified-Bessel-first-kind 𝜈 𝑧 1 2 𝜋 𝑖 superscript subscript 𝑖 𝜋 𝑖 𝜋 superscript 𝑒 𝑧 𝑡 𝜈 𝑡 𝑡 {\displaystyle{\displaystyle I_{\nu}\left(z\right)=\frac{1}{2\pi i}\int_{% \infty-i\pi}^{\infty+i\pi}e^{z\cosh t-\nu t}\mathrm{d}t,}}
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    DLMF id
    DLMF:10.32.E12
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    constraint
    | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}
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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.m2ajdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
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