DLMF:11.10.E1 (Q4018)

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DLMF:11.10.E1
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    Statements

    Defining formula
    𝐉 ν ⁡ ( z ) = 1 π ⁢ ∫ 0 π cos ⁡ ( ν ⁢ θ - z ⁢ sin ⁡ θ ) ⁢ d θ , Anger-J 𝜈 𝑧 1 𝜋 superscript subscript 0 𝜋 𝜈 𝜃 𝑧 𝜃 𝜃 {\displaystyle{\displaystyle\mathbf{J}_{\nu}\left(z\right)=\frac{1}{\pi}\int_{% 0}^{\pi}\cos\left(\nu\theta-z\sin\theta\right)\mathrm{d}\theta,}}
    0 references
    DLMF id
    DLMF:11.10.E1
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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.m2adec
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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.m1adec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
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