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Topic review (newest first)
What would you like to know?
I mean, about the Gamma function -- is it for a particular class?
I was just curious about the taylor series
You can also evaluate the integral numerically.
They will give you a (very good) approximation to the integral, yes.
So,will the taylor series give the same result as the integral's.
Sorry, I am wrong.. Ignore my previous post.
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?
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.
Ok,but it will be helpful to see a complex number example.
There are lots of ways to compute values for the gamma function. For example, this is a useful identity;
then it follows that
so you can use that to find values of the gamma function at 5/2, 7/2, etc.
Yes,different values and your explanation was clear but other values will make it easier for me to understand the way of approaching
You mean evaluating the gamma function at different values -- 0.75, 0.224, (3+2i), etc.?
I think if you show me some examples(such as other fractions and complex number)it will be easy for me to understand.