DLMF:10.56.E4 (Q3768)

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DLMF:10.56.E4
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    Statements

    test
    sinh ⁡ z 2 + 2 ⁢ i ⁢ z ⁢ t z = sinh ⁡ z z + ∑ n = 1 ∞ ( i ⁢ t ) n n ! ⁢ 𝗂 n - 1 ( 2 ) ⁡ ( z ) , superscript 𝑧 2 2 𝑖 𝑧 𝑡 𝑧 𝑧 𝑧 superscript subscript 𝑛 1 superscript 𝑖 𝑡 𝑛 𝑛 spherical-Bessel-I-2 𝑛 1 𝑧 {\displaystyle{\displaystyle\frac{\sinh\sqrt{z^{2}+2izt}}{z}=\frac{\sinh z}{z}% +\sum_{n=1}^{\infty}\frac{(it)^{n}}{n!}{\mathsf{i}^{(2)}_{n-1}}\left(z\right),}}
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    DLMF id
    DLMF:10.56.E4
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    Symbols used
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
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    hyperbolic sine function
    test
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2adec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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