p(z|ν) = (1/Γ(ν/2)) (1/2)^ν/2 z^ν/2-1 e^-z/2 ≡ γ(z;ν/2,1/2) , where z=Χ².

Its more familiar usage is in the cumulative form, which is just the incomplete gamma function. This is where you count off how much area is enclosed in [0,Χ²) to tell at what point the 68%, 95%, etc., thresholds are met. For example, for ν=1,

∫₀^Z dx p(Χ²|ν=1) = 0.68 when Z=1.

This is the origin of the ΔΧ²=1 method to determine error bars on best-fit parameters.