Comment #14 on issue 564 by pr...@goodok.ru: series expansion of acosh and
acoth
http://code.google.com/p/sympy/issues/detail?id=564
Regarding the wolframalpha.
I observed that it have many questions too, therefore can be considered as
etalon with accuracy.
Mathematically, `coth(0) == zoo` is true only in the case of when user asks
CAS about the extension of reals to complex numbers.
But I, e.g. can ask CAS to do not extend reals (then oo must the right
answer), or even can ask to extent reals to the similar so called
`semi-complex` numbers.
Second, coth(0) have singularity at this point:
And I supposed that walframalpha try to show this for us by returning `zoo`.
Or simply return `zoo` like
S(1)/S.Zero
oo
But I think that right way is return more general singularity description
(formally, coth(o) has no value, only infinite limit at this point)
So, the question, what coth(0) must result, I think is related with issue
2242 (A general way to describe and test for singularities) and so on.
Returning to the title of issue.
Both answers of sympy and maxima are correct.
Except the remarks about branches, but branches (multi-valued function) are
not used now for definitions of functions in sympy and it is a separated
question.
There is only definition what branches for multi-valued function are chosen
as main.
since the range of sinh(x) in the reals is (-1,1).
It is arguably.
--
You received this message because you are subscribed to the Google Groups
"sympy-issues" group.
To post to this group, send email to sympy-issues@googlegroups.com.
To unsubscribe from this group, send email to
sympy-issues+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/sympy-issues?hl=en.
