Formula:788

Digital Library of Mathematical Functions ID 2.5.E42

${\displaystyle{\displaystyle I_{2}(x)=\sum_{\Re\beta_{0}\leq\Re z\leq 1}\Residue\left[-x^{-z}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)\right]+\frac{1}{2\pi i}\int_{\rho-i\infty}^{\rho+i\infty}x^{-z}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)\mathrm{d}z.}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Mellin transform
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle\Residue}}$:
• ${\displaystyle{\displaystyle h(x)}}$: locally integrable function
• ${\displaystyle{\displaystyle I_{j}(x)}}$: integral
• ${\displaystyle{\displaystyle\rho}}$: parameter
 

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