ibeta(a,b,1) = 1 independent of the values of a, b.
But according to the definition ibeta(a,b,1) = gamma(a)*gamma(b)/gamma(a+b) this is not the case in this version:
gnuplot version 6.0 patchlevel 0 on ubuntu 24.04 LTS
Am I misunderstanding what ibeta(a,b,x) computes?
Alex van der Spek
[Earlier answer deleted. Sorry for any confusion if you read that first]
ibeta(a,b,x) is the normalized incomplete beta function β(a,b). The normalization means that it runs from 0 to 1.
normalized ibeta(a,b,x) = Γ(a+b)/(Γ(a)Γ(b) * [unnormalized ibeta(a,b,x)]
The documentation and demo may help:
https://gnuplot.sourceforge.net/demo_6.0/ibeta.html
Last edit: Ethan Merritt 2024-06-27
See edited answer. ibeta() is the normalized incomplete beta function.