I wasn't sure what you were trying to do. I couldn't find your definition for mathematicaDefinitionOfArcCoth
at the link you posted. The definition that I used was under Properties and Relations:
TrigToExp[ArcCoth[z]]
Out = -(1/2) Log[1-1/z]+1/2 Log[1+1/z]
But, something appears to be wrong with ArcCoth[-1/2]
when N
is applied or when using inexact arguments. It stays unevaluated with exact arguments outside of the domain.You should submit a bug report.