DLMF:8.6.E1 (Q2515)

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DLMF:8.6.E1
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    Statements

    Defining formula
    γ ⁡ ( a , z ) = z a sin ⁡ ( π ⁢ a ) ⁢ ∫ 0 π e z ⁢ cos ⁡ t ⁢ cos ⁡ ( a ⁢ t + z ⁢ sin ⁡ t ) ⁢ d t , incomplete-gamma 𝑎 𝑧 superscript 𝑧 𝑎 𝜋 𝑎 superscript subscript 0 𝜋 superscript 𝑒 𝑧 𝑡 𝑎 𝑡 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\gamma\left(a,z\right)=\frac{z^{a}}{\sin\left(\pi a% \right)}\int_{0}^{\pi}e^{z\cos t}\cos\left(at+z\sin t\right)\mathrm{d}t,}}
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    DLMF id
    DLMF:8.6.E1
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    constraint
    a ∉ ℤ 𝑎 {\displaystyle{\displaystyle a\notin\mathbb{Z}}}
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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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