Science Fair Projects Ideas - Beta function

All Science Fair Projects

 		      

Science Fair Project Encyclopedia for Schools!
  Search    Browse    Forum  Coach    Links    Editor    Help    Tell-a-Friend    Encyclopedia    Dictionary     

Science Fair Project Encyclopedia

For information on any area of science that interests you,
enter a keyword (eg. scientific method, molecule, cloud, carbohydrate etc.).
Or else, you can start by choosing any of the categories below.

Science Fair Project Encyclopedia Contents Page

Beta function

A separate article treats the beta-function (written with a hyphen) of physics.

In mathematics, the beta function (occasionally written as Beta function), also called the Euler integral of the first kind, is a special function defined by

\mathrm{\Beta}(x,y) = \int_0^1t^{x-1}(1-t)^{y-1}\,dt \!

for Re(x), Re(y) > 0. The beta function is symmetric, meaning that

\mathrm{\Beta}(x,y) = \mathrm{\Beta}(y,x). \!

It has many other forms, including:

\mathrm{\Beta}(x,y)=\frac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \!
\mathrm{\Beta}(x,y) = 2\int_0^{\pi/2}\sin^{2x-1}\theta\cos^{2y-1}\theta\,d\theta, \qquad \Re(x)>0,\ \Re(y)>0 \!
\mathrm{\Beta}(x,y) = \int_0^\infty\frac{t^{x-1}}{(1+t)^{x+y}}\,dt, \qquad \Re(x)>0,\ \Re(y)>0 \!
\mathrm{\Beta}(x,y) = \frac{1}{y}\sum_{n=0}^\infty(-1)^n\frac{(y)_{n+1}}{n!(x+n)} \!

where (x)n is the falling factorial. Euler's beta function was the first known scattering amplitude in string theory, first conjectured by Gabriele Veneziano .

See also

Last updated: 10-13-2005 13:52:36
Science Fair Project Encyclopedia Contents Page
12-03-2008 10:22:39
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
Science kits, science lessons, science toys, maths toys, hobby kits, science games and books - these are some of many products that can help give your kid an edge in their science fair projects, and develop a tremendous interest in the study of science. When shopping for a science kit or other supplies, make sure that you carefully review the features and quality of the products. Compare prices by going to several online stores. Read product reviews online or refer to magazines.

Start by looking for your science kit review or science toy review. Compare prices but remember, Price $ is not everything. Quality does matter.
Science Fair Coach
What do science fair judges look out for?
ScienceHound
Science Fair Projects for students of all ages
All Science Fair Projects.com Site
All Science Fair Projects Homepage
Search | Browse | Links | From-our-Editor | Books | Help | Contact | Privacy | Disclaimer | Copyright Notice