Comment #10 on issue 564 by [email protected]: series expansion of acosh and acoth
http://code.google.com/p/sympy/issues/detail?id=564
It looks like I was mistaken. Some of the branch cuts follow from using the principal branch of the complex logarithm, but all of the complex trig functions, hyperbolic trig functions and their inverses are analytic continuations of their real counterparts defined in the usual ways. I think it's just that the inverses that are being extended involve logarithms. In some cases they run across the branch cut as in atanh(x) (which is otherwise continuous for all real x), but others don't like asinh(x). For real x, x + Sqrt(1 + x**2) can never be in (-oo, 0]. But since we're extending the real version of asinh(x) we can't define it on (-oo, -1] or [1, oo) since the range of sinh(x) in the reals is (-1,1).
In any case, it looks like principal branches are somewhat standardized. For defining the functions I could just pick a specific source and then reference it in the documentation.
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