DLMF:10.35.E2 (Q3551)

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DLMF:10.35.E2
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    Statements

    Defining formula
    e z ⁢ cos ⁡ θ = I 0 ⁡ ( z ) + 2 ⁢ ∑ k = 1 ∞ I k ⁡ ( z ) ⁢ cos ⁡ ( k ⁢ θ ) , superscript 𝑒 𝑧 𝜃 modified-Bessel-first-kind 0 𝑧 2 superscript subscript 𝑘 1 modified-Bessel-first-kind 𝑘 𝑧 𝑘 𝜃 {\displaystyle{\displaystyle e^{z\cos\theta}=I_{0}\left(z\right)+2\sum_{k=1}^{% \infty}I_{k}\left(z\right)\cos\left(k\theta\right),}}
    0 references
    DLMF id
    DLMF:10.35.E2
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    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    modified Bessel function of the first kind
    Defining formula
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2aadec
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    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1dec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1adec
    0 references
     
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