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 August 21st, 2013, 05:01 AM #1 Senior Member   Joined: Oct 2012 Posts: 460 Thanks: 0 gama vs ß function plots Dear All! Please, is it possible to distinguish ß and gama function plot on the first look, and how? Many thanks!
 August 21st, 2013, 06:19 PM #2 Math Team     Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions Re: gama vs ß function plots Could you illustrate the question ? Do you mean you are given the two graphs of the functions and asked to choose which one is for gamma or beta ?
 August 22nd, 2013, 07:41 AM #3 Senior Member   Joined: Oct 2012 Posts: 460 Thanks: 0 Re: gama vs ß function plots Yes, right this_ if it is possible to see the difference form the graph
 August 22nd, 2013, 02:20 PM #4 Math Team     Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions Re: gama vs ß function plots Ok ,let us see : The beta function is defined in terms of gamma function as follows $\beta(x,y)= \frac{\Gamma(x) \Gamma(y) }{\Gamma(x+y)}$ So the beta function requires to insert two values $x,y$ . The representation using gamma function is so interesting because we can benefit from the values of Gamma function . It is known that the gamma function has isolated singularities (or poles ) at negative integers and zero . That is to be understood using the following equation $\Gamma(x)= \lim_{n\to \infty }\frac{n! n^x }{x(x+1)(x+2) \cdots (x+n) }$ So the function will explode at these values . Of course the graph of beta function on the other hand cannot be drown on the 2-D space because we have two inputs . Suppose on the other hand we fixed some values $\beta(x,1)= \frac{\Gamma(x) }{\Gamma(x+1)}=\frac{1}{x}$ Defined on the whole space except at 0 $\beta(x,\frac{1}{2})= \frac{ \sqrt{\pi } \Gamma(x) }{\Gamma(x+\frac{1}{2})}$ Defined on the whole space except at negative integers , 0, -1/2 .

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