Generalizing the previous question: Define Log so that negative reals evaluate on lower edge of branch
For real positive values $x>1$, Mathematica's polylogarithm function
PolyLog[2, x] yields a result whose imaginary part is negative (because it is defined to be evaluated just below the cut).
In := PolyLog[2, 1.6] Out = 2.41313 - 1.47656 I
In the spirit of the previous question (linked above) what is the cleanest way to get Mathematica to evaluate the function just above the cut, so that I get a positive imaginary part?
Out = 2.41313 + 1.47656 I
PolyLog appears inside the definition of a larger function that I am using. I need to use this function for both analytic and numeric purposes. I should be able to evaluate it numerically, and also be able to differentiate it without giving a lot of non-analytic garbage associated with the deserved change. Is there anything I can do so that I get both properties?