Gaussian function: Difference between revisions

Revision as of 20:29, 25 February 2014

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-In [[mathematics]], there are two types of '''Euler integral''':<ref>Jeffrey, Alan; and Dai, Hui-Hui (2008).  Handbook of Mathematical Formulas 4th Ed. Academic Press. ISBN 978-0-12-374288-9. pp. 234-235</ref>
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-: 1. ''Euler [[integral]] of the first kind'': the [[Beta function]]
-:: <math>\mathrm{\Beta}(x,y)= \int_0^1t^{x-1}(1-t)^{y-1}\,dt =\frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}</math>
-: 2. ''Euler integral of the second kind'': the [[Gamma function]]
-:: <math>\Gamma(z) = \int_0^\infty  t^{z-1}\,e^{-t}\,dt</math>
-For [[natural number|positive integer]]s ''m'' and ''n''
-:<math>\mathrm{\Beta}(n,m)= {(n-1)!(m-1)! \over (n+m-1)!}={n+m \over nm{n+m \choose n}}</math>
-:<math>\Gamma(n) = (n-1)! \,</math>
-==See also==
-*[[Euler integral (thermodynamics)]]
-*[[Leonhard Euler]]
-*[[List of topics named after Leonhard Euler]]
-==References==
-{{Reflist}}
-[[Category:Gamma and related functions]]
-{{sia}}