Formula:786

Digital Library of Mathematical Functions ID 2.5.E40

${\displaystyle{\displaystyle I_{j}(x)=\frac{1}{2\pi i}\int_{p_{j}-i\infty}^{p_{j}+i\infty}x^{-z}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu h_{j}\mskip 3.0mu \left(z\right)\mathrm{d}z,}}$

Constraint(s)

${\displaystyle{\displaystyle j=1,2}}$

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
• ${\displaystyle{\displaystyle h(x)}}$: locally integrable function
• ${\displaystyle{\displaystyle I_{j}(x)}}$: integral
• ${\displaystyle{\displaystyle p_{j}}}$: real numbers
 

Resources that cite this formula

No records found.