Re: Re: Euler's Gamma and Beta Functions
- To: mathgroup at smc.vnet.net
- Subject: [mg41402] Re: [mg41392] Re: Euler's Gamma and Beta Functions
- From: Selwyn Hollis <selwynh at earthlink.net>
- Date: Sun, 18 May 2003 05:02:14 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
For an earlier and more elementary example, you'll find the following in typical elementary differential equations texts: Integer-order Bessel functions are defined as certain power series with coefficients that involve factorials. The Gamma function is necessary to extend these to fractional orders. I suspect that this is the first context in which the Gamma function appeared. ----- Selwyn Hollis http://www.math.armstrong.edu/faculty/hollis On Saturday, May 17, 2003, at 05:51 AM, Dr. Wolfgang Hintze wrote: > Raz, > > the Euler Beta function appeared in elementary particle physics as a > model for the scattering amplitude in the so called "dual resonance > model". Introduced by Veneziano in the 1970th in order to fit > experimeltal data it soon turned out that the basic physics behind this > model is the string (instead of the zero-dimensional mass point). I > recommend to look for "string theory, history" on the internet. > > Hope this helps. > > Regards, > Wolfgang > > RazroRog wrote: > >> Hello friends, >> >> Please forgive me - I know I will be asking questions that to you will >> appear stupid. I do applogize for that. I'm working through Mr. >> Wolfram's >> book - page by page. I love this Mathematica program and the book is >> very >> well designed. I am just trying to learn. >> >> I need to know about Euler's Gamma and Beta functions. I understand >> the >> attempt to generalize the factorial and how the Beta function arose >> but >> could you show me a few examples from physics and/or engineering how >> these >> functions are useful? I need to get a feel for them. >> >> Thank you very much, >> >> Raz >> >> >> >> > > >