Give references for branch cuts in various symbolic functions

[kcrisman]

See #9900, where conjugation is improved but relies on a choice of branch cut. If we can find internet/book references for whether these are 'standard', that would be a nice addition to our documentation. Also, let's make sure they are consistent with our numerical evaluation!

CC: @burcin

Component: documentation

Issue created by migration from https://trac.sagemath.org/ticket/10033

[jpflori]

comment:1

Here is a reference (available online !):

Abramowitz and Stegun: Handbook of Mathematical Functions

Branch cuts are given in chapter 4. Elementary Transcendental Functions. Pages 67 (for log), 79 (for inverse trig func) and 86 (for inverse hyper fun) are of special interest.

A good link on the web :

• GSL http://www.gnu.org/software/gsl/manual/html_node/Complex-Numbers.html which refers to the above one and some from below

Here are some other links on the internet :

• Mathworld: http://mathworld.wolfram.com/BranchCut.html which refers to Mathematica
• GNU emacs Calc: http://www.delorie.com/gnu/docs/calc/calc_217.html referring to Mathematica
• Numpy : http://docs.scipy.org/doc/numpy/reference/generated/numpy.arccosh.html

[jpflori]

comment:2

And the url of the book which I forgot to include in the previous post:

http://www.math.sfu.ca/~cbm/aands/