Timeline for Why is the Gamma function shifted from the factorial by 1?
Current License: CC BY-SA 2.5
5 events
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| Dec 27, 2021 at 1:27 | comment | added | Michael Hardy | @KevinCasto : But in that case the expected value of a random variable whose probability density is that function of $t$ on the interval $(0,1)$ would NOT be $x/(x+y). \qquad$ | |
| Apr 14, 2014 at 15:58 | comment | added | Sergei | But not only two of them. There are much more factorial generalizations which interpolate integer factorials. End even have not poles! For example the Hadamard generalization of factorials, look on Wolfram. | |
| Apr 11, 2010 at 3:10 | comment | added | Kevin Casto | The thing is, the Beta function is itself (to me) incorrectly defined; it should be the integral of t^x*(1-t)^y. Likewise, there doesn't seem to be any reason why, in the generalization to characters, we can't have J be the analog of B' (where B'(x,y) = B(x+1,y+1)) and g the analog of Pi. | |
| Apr 11, 2010 at 2:30 | history | edited | castal | CC BY-SA 2.5 |
Google books doesn't seem to take you all the way to the target page.
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| Apr 11, 2010 at 2:22 | history | answered | castal | CC BY-SA 2.5 |