DLMF:8.19.E25 (Q2711)

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DLMF:8.19.E25
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    Statements

    Defining formula
    ∫ 0 ∞ e - a ⁢ t ⁢ t b - 1 ⁢ E p ⁡ ( t ) ⁢ d t = Γ ⁡ ( b ) ⁢ ( 1 + a ) - b p + b - 1 ⁢ F ⁡ ( 1 , b ; p + b ; a / ( 1 + a ) ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 superscript 𝑡 𝑏 1 exponential-integral-En 𝑝 𝑡 𝑡 Euler-Gamma 𝑏 superscript 1 𝑎 𝑏 𝑝 𝑏 1 Gauss-hypergeometric-F 1 𝑏 𝑝 𝑏 𝑎 1 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}t^{b-1}E_{p}\left(t\right)% \mathrm{d}t=\frac{\Gamma\left(b\right)(1+a)^{-b}}{p+b-1}\*F\left(1,b;p+b;a/(1+% a)\right),}}
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    DLMF id
    DLMF:8.19.E25
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