Residue Formula for Exponential Fraction with Constant Terms

[Alamino]

Is there a simple formula for the residue of

$$\frac{e^{ik}}{\prod_j (k-is_j)}$$

where $$s_j$$ are constants ?

 

[Tide]

Is there a simple formula for the residue of

$$\frac{e^{ik}}{\prod_j (k-is_j)}$$

where $$s_j$$ are constants ?

I assume your variable of integration is k - correct accordingly if it is not. The residue will be just the sum over n of
$$\frac{e^{s_n}}{\prod_{j \neq n} (i s_n-is_j)}$$

 

[Alamino]

Thank you, that's exactly what wanted.