Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,590

How about playing with some numbers?

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**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

well i know that Gamma(1/2) is sqrt(pi) but i don't know how that would help.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,590

Try good ole substitution.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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substitution with what? Gamma(n+1)?

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,590

How about using one of the most advanced techniques ever discovered. Totally unknown to modern mathematicians.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

and that is???

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,590

Try plugging in some numbers!

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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it looks like it's going towards 1!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,590

Yes! A fantastic answer. Brilliant in every sense of the word. I love it. It is the same answer I got so long ago!

Unfortunately it is wrong.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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why is it wrong?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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I bet you plugged in nothing but even numbers. Try an odd number...

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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-1!!! so it's indeterminate???

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**bobbym****Administrator**- From: Bumpkinland
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The limit does not exist because we do not know what the parity of infinity is.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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that's what i meant.

but is there a way to prove it other than just trying out numbers?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Not one I know of.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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well i think that if we prove that Gamma(1/2-n) has different signs when the parity of n changes,the non-existence is just a consequence.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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That oscillates but...

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**anonimnystefy****Real Member**- From: The Foundation
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but what?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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I thought there was another term involving the Gamma function that you left out.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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well there is,but it is always positive.

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**bobbym****Administrator**- From: Bumpkinland
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You will need to prove that too.

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**anonimnystefy****Real Member**- From: The Foundation
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yeah,you're right.but if we can prove that,than the limit won't exist.

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**bobbym****Administrator**- From: Bumpkinland
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There is one demonstration shown to me where the problem is reduced to

I do not remember how that was done.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

too bad.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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I did not like his proof anyway.

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