DLMF:10.56.E3 (Q3767)

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DLMF:10.56.E3
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    test
    cosh ⁡ z 2 + 2 ⁢ i ⁢ z ⁢ t z = cosh ⁡ z z + ∑ n = 1 ∞ ( i ⁢ t ) n n ! ⁢ 𝗂 n - 1 ( 1 ) ⁡ ( z ) , superscript 𝑧 2 2 𝑖 𝑧 𝑡 𝑧 𝑧 𝑧 superscript subscript 𝑛 1 superscript 𝑖 𝑡 𝑛 𝑛 spherical-Bessel-I-1 𝑛 1 𝑧 {\displaystyle{\displaystyle\frac{\cosh\sqrt{z^{2}+2izt}}{z}=\frac{\cosh z}{z}% +\sum_{n=1}^{\infty}\frac{(it)^{n}}{n!}{\mathsf{i}^{(1)}_{n-1}}\left(z\right),}}
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    DLMF id
    DLMF:10.56.E3
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    Symbols used
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
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    hyperbolic cosine function
    test
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2adec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    modified spherical Bessel function
    test
    𝗂 n ( 1 ) ⁡ ( z ) spherical-Bessel-I-1 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E7.m2adec
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    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1bdec
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    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1bdec
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