DLMF:10.32.E12 (Q3532)

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DLMF:10.32.E12
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    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:10.32.E12
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    | ph z | < 1 2 π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2ajdec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1akdec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2agdec
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    cosh z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    C4.S28.E2.m2aedec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2adec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3akdec
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    I ν ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S25.E2.m2addec
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    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    C1.S9.E7.m1aedec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1idec
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