Skew-t Distribution LPDF

Hi, I’m building a model where I need the lcdf of a skew-t. Below is the pdf form of Skew-t,
Azzalini develops this function in R in package sn with the name of pst.
If anyone can help me write this lcdf in stan I would appreciate it a lot.

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Thanks but the parameterization I use has -Inf <lambda <Inf. I forgot to inform you that
If anyone else can help me I’ll appreciate it.