DLMF:3.4.E19 (Q1223)

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DLMF:3.4.E19
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    Statements

    Defining formula
    1 k ! = 1 2 ⁢ π ⁢ r k ⁢ ∫ 0 2 ⁢ π e r ⁢ cos ⁡ θ ⁢ cos ⁡ ( r ⁢ sin ⁡ θ - k ⁢ θ ) ⁢ d θ . 1 𝑘 1 2 superscript 𝑟 𝑘 superscript subscript 0 2 superscript 𝑒 𝑟 𝜃 𝑟 𝜃 𝑘 𝜃 𝜃 {\displaystyle{\displaystyle\frac{1}{k!}=\frac{1}{2\pi r^{k}}\int_{0}^{2\pi}e^% {r\cos\theta}\cos\left(r\sin\theta-k\theta\right)\mathrm{d}\theta.}}
    0 references
    DLMF id
    DLMF:3.4.E19
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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.m2abdec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
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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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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
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    Q11165
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C3.S4.XMD4.m1adec
    0 references
     
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