Comment #3 on issue 2247 by [email protected]: Problem with coth
http://code.google.com/p/sympy/issues/detail?id=2247

There's no foliation in these cases so there's no need in cuts of Rieman surface:
tanh(acoth(x))=1/x
coth(atanh(x))=1/x
coth(acoth(x))=x

The others is agreed with sqrt foliation, because

sqrt(4)
2

Let's proove this formula coth(asinh(x))=sqrt(x**2+1)/x
asinh(x)=t so by definition sinh(t)=x
coth(t)**2=cosh(t)**2/sinh(t)**2=(1+sinh(t)**2)/sinh(t)**2=(1+x**2)/x**2
as positive branch of sqrt are chosen than coth(t)=sqrt(1+x**2)/x
So it seems we should not think about issue's 564 agreement.

Sorry if I present too much details.

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