DLMF:2.5.E41 (Q817): Difference between revisions

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DLMF:2.5.E41
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    Statements

    Defining formula
    I 1 ⁢ ( x ) = ℳ ⁡ h 1 ⁡ ( 1 ) ⁢ x - 1 + 1 2 ⁢ π ⁢ i ⁢ ∫ ρ - i ⁢ ∞ ρ + i ⁢ ∞ x - z ⁢ Γ ⁡ ( 1 - z ) ⁢ ℳ ⁡ h 1 ⁡ ( z ) ⁢ d z , subscript 𝐼 1 𝑥 Mellin-transform subscript ℎ 1 1 superscript 𝑥 1 1 2 𝜋 𝑖 superscript subscript 𝜌 𝑖 𝜌 𝑖 superscript 𝑥 𝑧 Euler-Gamma 1 𝑧 Mellin-transform subscript ℎ 1 𝑧 𝑧 {\displaystyle{\displaystyle I_{1}(x)=\mathscr{M}\mskip-3.0mu h_{1}\mskip 3.0% mu \left(1\right)x^{-1}+\frac{1}{2\pi i}\int_{\rho-i\infty}^{\rho+i\infty}x^{-% z}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu h_{1}\mskip 3.0mu \left(z% \right)\mathrm{d}z,}}
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    DLMF id
    DLMF:2.5.E41
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