Formula:3427

Digital Library of Mathematical Functions ID 8.21.E8

${\displaystyle{\displaystyle\mathrm{Si}\left(a,z\right)=\Gamma\left(a\right)\sin\left(\tfrac{1}{2}\pi a\right)-\mathrm{si}\left(a,z\right),}}$

Constraint(s)

${\displaystyle{\displaystyle a\neq-1,-3,-5,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{a},\NVar{z}\right)}}$: generalized sine integral
• ${\displaystyle{\displaystyle\mathrm{si}\left(\NVar{a},\NVar{z}\right)}}$: generalized sine integral
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a}}$: parameter
 

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