[is an odd function of t.] This is subtle. Mathematica plots the real part odd and the imaginary part even! gosper.org/reim ln tan.png Is Mathematica wrong? Julian writes "No. To make it an odd function, you need to make choices about branches of the composition of log and tan, while mathematica has a standard choice of branch for log which it is applying; this is the correct behavior." Thus igd(t) is so "darn strange" that it is odd but doesn't look it. Said more carefully, igd(2t) is not identically equal to log(tan(t+pi/4)). --rwg On 2016-07-27 21:53, rcs@xmission.com wrote:

Assuming you mean log(tan(t+pi/4)), this is igd(2t), inverse gudermannian of 2t, which is an odd function for small t. To see this without appealing to special functions, notice that (switching to degrees)

tan(45+x) = cot(45-x)

since the angles sum to 90. Using cot == 1/tan, and applying the log, we get

log(tan(45+x)) = - log(tan(45-x)).

Rich

------- Quoting Dan Asimov <dasimov@earthlink.net>:

...

is an odd function of t? -----

It's pretty darn strange, no doubt about it.

?Dan