a contour integral device
Hi, I'm reading a book and I need to know how to evaluate this integral :
[TEX]\frac{1}{2\pi i}\int_{ci\infty}^{c+i\infty}\frac{y^s}{s}ds[/TEX] / \frac{1}{2\pi i}\int_{ci\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? 
[QUOTE=wildrabbitt;609373]Hi, I'm reading a book and I need to know how to evaluate this integral :
[TEX]\frac{1}{2\pi i}\int_{ci\infty}^{c+i\infty}\frac{y^s}{s}ds[/TEX] / \frac{1}{2\pi i}\int_{ci\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?[/QUOTE] Encapsulate the \(\LaTeX\) in backslash left braket and backslash right bracket. For inline use parentheses. \[\frac{1}{2\pi i}\int_{ci\infty}^{c+i\infty}\frac{y^s}{s}ds\] 
Thanks.

[QUOTE=wildrabbitt;609373]Perhaps someone recognises it and knows a page online or a book where I could find it?[/QUOTE]
This (without the easier y=1 case) is a lemma that appears in the proof of [URL="https://en.wikipedia.org/wiki/Perron%27s_formula"]Perron's formula[/URL]. [URL="https://abel.math.harvard.edu/archive/213b_spring_05/perron_formula_without_error_estimate.pdf"]Here[/URL] is a reference I found. 
Thanks a lot. That's just the sort of thing I was looking for.

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