a contour integral device

[wildrabbitt]

Hi, I'm reading a book and I need to know how to evaluate this integral :






/ \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\frac{y^s}{s}ds forgotten how to get latex in a post again

I know it equals 0 on (0,1), 1/2 for y = 1 and 1 for y > 1 but I can't find a proof anywhere.


Perhaps someone recognises it and knows a page online or a book where I could find it?

[paulunderwood]

Originally Posted by wildrabbitt

Hi, I'm reading a book and I need to know how to evaluate this integral :






/ \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\frac{y^s}{s}ds forgotten how to get latex in a post again

I know it equals 0 on (0,1), 1/2 for y = 1 and 1 for y > 1 but I can't find a proof anywhere.


Perhaps someone recognises it and knows a page online or a book where I could find it?

Encapsulate the \(\LaTeX\) in backslash left braket and backslash right bracket. For inline use parentheses.

\[\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\frac{y^s}{s}ds\]

[wildrabbitt]

Thanks.

[charybdis]

Originally Posted by wildrabbitt

Perhaps someone recognises it and knows a page online or a book where I could find it?

This (without the easier y=1 case) is a lemma that appears in the proof of Perron's formula. Here is a reference I found.

[wildrabbitt]

Thanks a lot. That's just the sort of thing I was looking for.