Show that for and the integral converges.

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- May 8th 2011, 09:34 AMEinStoneConvergence of Integral
Show that for and the integral converges.

- May 8th 2011, 11:18 AMgirdav
You can begin to show that the sequence where is convergent.

- May 8th 2011, 12:51 PMEinStone
Well that is exactly what I want to show, I need some hint or maybe some criterion to use.

- May 8th 2011, 01:46 PMgirdav
If we denote s =u+iv we have hence hence we only have to show the result if is a positive real number.

It's true if because and are convergent. If use the fact that the sequence is convergent. For , use inequalities involving and . - May 8th 2011, 03:26 PMEinStone
Ok, I derived something similar already as well, but for I really don't see how to show that converges.

- May 9th 2011, 03:07 AMgirdav
The function is decreasing hence . We have

which is convergent (we don't have to distinguish the case or not, so it's better than my previous work). - May 9th 2011, 03:16 AMEinStone
ok, this looks good, but what are the <br/>'s and what is exactly is u?

- May 9th 2011, 03:44 AMgirdav
I don't know what <br/>'s are (maybe this come from latex issue). s=u+iv, I forgot it.