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# Showing inequalities (Context is gamma function converging) watch

1. I'm not after another proof.

I've just got a couple of inequalities

I don't know how to show when following a given proof in my book.

These are:

Q1)

So this is obvioulsy true, however I think I'm being dumb because surely this is true for all (the integral over the gamma function is split into and ) and so this inequality is used in the latter, but I don't see why it can't be used in the former, e.g is also true isn't it? and as this is also true, because the LHS ..

Q2) that for
I am unsure how to show this, or understand why it holds,and then secondly I need to show that I can write I am unsure what to do next or whether this helps

2. (Original post by xfootiecrazeesarax)
Q1)
This is true, as you can (carefully) cancel off the from both sides and you are left with something nice and easy.

Q2) that for
This is not true in general. Choose x = 2 and t = 4, for example.
3. (Original post by Gregorius)
This is true, as you can (carefully) cancel off the from both sides and you are left with something nice and easy.

This is not true in general. Choose x = 2 and t = 4, for example.
ahh okay, thanks. I was trying to follow the proof here:

http://math.stackexchange.com/questi...onverges-for-z

the first answer...so this is incorrect? or ok for large
4. (Original post by xfootiecrazeesarax)
ahh okay, thanks. I was trying to follow the proof here:

http://math.stackexchange.com/questi...onverges-for-z

the first answer...so this is incorrect? or ok for large
It's incorrect for general x, but true for large x (i.e. as x->infinity). (If you read the entire thread, you'll see various comments to this effect).
5. (Original post by DFranklin)
It's incorrect for general x, but true for large x (i.e. as x->infinity). (If you read the entire thread, you'll see various comments to this effect).
Okay thanks.

And yet the integral inequality still holds because the behaviour at dominates over the small behaviour?
6. anyone on how to prove q2?

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