DLMF:13.10.E4 (Q4463)

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DLMF:13.10.E4
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    Statements

    test
    ∫ 0 ∞ e - z ⁢ t ⁢ t b - 1 ⁢ 𝐌 ⁡ ( a , b , t ) ⁢ d t = z - b ⁢ ( 1 - 1 z ) - a , superscript subscript 0 superscript 𝑒 𝑧 𝑡 superscript 𝑡 𝑏 1 Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑡 𝑡 superscript 𝑧 𝑏 superscript 1 1 𝑧 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt}t^{b-1}{\mathbf{M}}\left(a% ,b,t\right)\mathrm{d}t=z^{-b}\left(1-\frac{1}{z}\right)^{-a},}}
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    DLMF id
    DLMF:13.10.E4
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    constraint
    ℜ ⁡ b > 0 𝑏 0 {\displaystyle{\displaystyle\Re b>0}}
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