Comment #8 on issue 564 by jpmccaff...@gmail.com: series expansion of acosh
and acoth
http://code.google.com/p/sympy/issues/detail?id=564
That's an interesting question. If you look at the inverse hyperbolic
functions they're all defined as logarithms of something and the standard
choice for principal branch cut for the logarithm is (-oo, 0]. The
hyperbolic branch cuts follow directly from that. For example if you look at
atanh(x) = (1/2)* ( log(1+x) - log(1-x) )
The values on its branch cut, (-oo, 1] and [1, oo) are precisely the values
that would map onto the principal branch cut for one of the two logarithms
in the expression. So the Hyperbolic branch cuts are just the cuts that map
onto the principal branch cut for the logarithm.
I'm not sure how the standard inverse trig functions play out but I'll look
into it later tonight.
On a related note, is there some specific reason that sech, csch, asech and
acsch are not implemented? If not, I'd be happy to put them together.
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