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

You are not logged in. #1 20121021 23:53:10
Gamma functionI want to know about gamma function,I have read about it in wikipedia,but I could not understand it very much,so please help(I know about factorial). #2 20121022 00:40:15
Re: Gamma functionHi Sabbir; so Gamma(5) = 4! = 24. The gamma function also defined for other than integers. But that is all in the pages you visited. Do you have a specific problem that requires the Gamma function? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20121022 00:43:24
Re: Gamma functionWhat do you need help with? or . This integral can be annoying to evaluate, so quite often people use a table of values, or use some known properties of distributions to solve. For simplicity, let's try to evaluate Gamma(0.5). I'll rewrite this as I'll make a substitution; So our integral becomes Do you recognise this integral? It is a disguised form of something called the Gaussian integral. It's defined as Since it's an even function (it's symmetrical about the yaxis), the area from 0 to infinity is just half of the area from negative infinity to positive infinity. Thus, your integral evaluates to √π. Hope this helps! #4 20121022 00:51:43
Re: Gamma functionYou can also evaluate the Gaussian integral using polar coordinates (rather than just accepting my definition for it). It's a bit long but I can show you if you'd like. #5 20121022 01:07:05
Re: Gamma functionI think if you show me some examples(such as other fractions and complex number)it will be easy for me to understand. #6 20121022 01:10:02
Re: Gamma functionYou mean evaluating the gamma function at different values  0.75, 0.224, (3+2i), etc.? #7 20121022 01:35:47
Re: Gamma functionYes,different values and your explanation was clear but other values will make it easier for me to understand the way of approaching #8 20121022 01:53:05
Re: Gamma functionHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20121022 01:56:24
Re: Gamma functionThere 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. #11 20121022 02:07:21
Re: Gamma functionThose 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. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #12 20121022 02:11:46
Re: Gamma functionEvaluating 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 e^{i} is just a constant. Can you see where to go from here? #14 20121022 02:41:30
Re: Gamma functionSo,will the taylor series give the same result as the integral's. #15 20121022 02:47:19
Re: Gamma function
They will give you a (very good) approximation to the integral, yes. #16 20121022 02:52:18
Re: Gamma functionYou can also evaluate the integral numerically. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #18 20121022 03:02:44
Re: Gamma function
I mean, about the Gamma function  is it for a particular class? #19 20121022 08:48:48
Re: Gamma functionHi;
What would you like to know? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 