mersenneforum.org a contour integral device
 Register FAQ Search Today's Posts Mark Forums Read

 2022-07-12, 17:52 #1 wildrabbitt   Jul 2014 2·32·52 Posts a contour integral device Hi, I'm reading a book and I need to know how to evaluate this integral : $\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\frac{y^s}{s}ds$ / \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? Last fiddled with by wildrabbitt on 2022-07-12 at 17:59
2022-07-12, 18:37   #2
paulunderwood

Sep 2002
Database er0rr

102348 Posts

Quote:
 Originally Posted by wildrabbitt Hi, I'm reading a book and I need to know how to evaluate this integral : $\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\frac{y^s}{s}ds$ / \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.

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

Last fiddled with by paulunderwood on 2022-07-12 at 18:43

 2022-07-12, 19:50 #3 wildrabbitt   Jul 2014 2×32×52 Posts Thanks.
2022-07-12, 22:55   #4
charybdis

Apr 2020

11000111012 Posts

Quote:
 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.

 2022-07-13, 06:13 #5 wildrabbitt   Jul 2014 2×32×52 Posts Thanks a lot. That's just the sort of thing I was looking for.

 Similar Threads Thread Thread Starter Forum Replies Last Post a1call Lounge 4 2019-09-15 17:05 Uncwilly Soap Box 2 2019-05-02 16:06 jasong jasong 8 2014-10-16 05:14 jasong jasong 24 2013-06-05 21:31 jasong jasong 10 2012-03-05 07:31

All times are UTC. The time now is 20:59.

Tue Aug 9 20:59:15 UTC 2022 up 33 days, 15:46, 2 users, load averages: 1.06, 1.03, 1.11