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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

bobbym
2012-10-22 08:48:48

Hi;

I was just curious about the taylor series

What would you like to know?

zetafunc.
2012-10-22 03:02:44

Sabbir wrote:

I was just curious about the taylor series

I mean, about the Gamma function -- is it for a particular class?

Sabbir
2012-10-22 03:00:38

I was just curious about the taylor series

bobbym
2012-10-22 02:52:18

You can also evaluate the integral numerically.

zetafunc.
2012-10-22 02:47:19

Sabbir wrote:

So,will the taylor series give the same result as the integral's.

They will give you a (very good) approximation to the integral, yes.

May I ask what this is for?

Sabbir
2012-10-22 02:41:30

So,will the taylor series give the same result as the integral's.

zetafunc.
2012-10-22 02:14:44

Sorry, I am wrong.

. Ignore my previous post.

zetafunc.
2012-10-22 02:11:46

Evaluating it at complex numbers is interesting. Let's try to find Gamma(1+i).



but note that



so our integral becomes



I can do that becaues ei is just a constant. Can you see where to go from here?

bobbym
2012-10-22 02:07:21

Those get very complicated. One way is with a Taylor series expanded around infinity.









This is quite close for only two terms of a Taylor series.

Sabbir
2012-10-22 02:00:29

Ok,but it will be helpful to see a complex number example.

zetafunc.
2012-10-22 01:56:24

There are lots of ways to compute values for the gamma function. For example, this is a useful identity;



Thus, since



then it follows that



so you can use that to find values of the gamma function at 5/2, 7/2, etc.

bobbym
2012-10-22 01:53:05

Hi;

Only certain values yield nice results like that. For say Gamma(10 + 1/3 ) you will have to resort to numerical methods.

Sabbir
2012-10-22 01:35:47

Yes,different values and your explanation was clear but other values will make it easier for me to understand the way of approaching

zetafunc.
2012-10-22 01:10:02

You mean evaluating the gamma function at different values -- 0.75, 0.224, (3+2i), etc.?

Was any part of my explanation unclear?

Sabbir
2012-10-22 01:07:05

I think if you show me some examples(such as other fractions and complex number)it will be easy for me to understand.

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