DLMF:8.6.E8 (Q2522)

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DLMF:8.6.E8
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    Statements

    Defining formula
    γ ⁡ ( a , z ) = - i ⁢ z a 2 ⁢ sin ⁡ ( π ⁢ a ) ⁢ ∫ - 1 ( 0 + ) t a - 1 ⁢ e z ⁢ t ⁢ d t , incomplete-gamma 𝑎 𝑧 imaginary-unit superscript 𝑧 𝑎 2 𝜋 𝑎 superscript subscript 1 limit-from 0 superscript 𝑡 𝑎 1 superscript 𝑒 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\gamma\left(a,z\right)=\frac{-\mathrm{i}z^{a}}{2% \sin\left(\pi a\right)}\int_{-1}^{(0+)}t^{a-1}e^{zt}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:8.6.E8
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    constraint
    a ∉ ℤ 𝑎 {\displaystyle{\displaystyle a\notin\mathbb{Z}}}
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    z ≠ 0 𝑧 0 {\displaystyle{\displaystyle z\neq 0}}
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    a ∉ ℤ 𝑎 ℤ {\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.m2abdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
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