20101124, 14:58  #1 
Sep 2010
3^{3} Posts 
Gamma function
It would be much more elegant to define gamma(z) = z!, but mathematicians prefer gamma(z) = (z1)! and clutter a really beautiful improper integral with an awkwardly placed minus one.
Why? 
20101124, 22:07  #2 
"William"
May 2003
New Haven
2×3^{2}×131 Posts 
Look up the integral definition of gamma. Something like this is necessary because Gamma is defined for reals (except negative integers). Your proposal would destroy the elegance of this definition. Your perception of elegance comes from only knowing the factorial correspondence. The gamma function has many other uses, and deserves elegance within its own domain.

20101125, 03:42  #3  
Aug 2006
2^{2}×5×293 Posts 
Quote:


20101125, 04:10  #4 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
2^{6}·67 Posts 
If you make gamma(z)=z! how would you distinguish it from factorial(z)?

20101125, 14:31  #5  
Sep 2010
3^{3} Posts 
Quote:
Egg, face, case in point. :) Any idea why they eventually did settle for the z1, instead of just plain z in the integral definition? 

20101207, 20:49  #6 
Dec 2008
you know...around...
2^{2}×7×19 Posts 
I asked myself the same question when I learned about that function, and was even more confused about psi(n) = (value of the harmonic series at n1)  0,5772156649... (the EulerMascheroniConstant).
But I always trusted that there is a just reason for it and tried to learn more about it. Am I wise, or what? 
20101223, 22:18  #7 
"Gang aft agley"
Sep 2002
2·1,877 Posts 

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