#2718 Incomplete beta function at x=1 returns 1.0 always

[Anonymous]

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

[Ethan Merritt]

[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

[Ethan Merritt]

See edited answer. ibeta() is the normalized incomplete beta function.