# [Maxima] dilogarithm float for complex arg?

Raymond Toy toy.raymond at gmail.com
Thu Apr 26 14:32:43 CDT 2012

```On Thu, Apr 26, 2012 at 11:27 AM, Edwin Woollett <woollett at charter.net>wrote:

>
> An integral which returns an expression in terms
> of the dilogarithm function Li[2](z), in which z is
> in general complex, is
> ------------------------------**-------------
> (%i11) integrate(log(sin(x)),x,1,2);
>
> (%o11) -2*%i*atan(sin(2)/(cos(2)+1))-**2*%i*atan(sin(2)/(cos(2)-1))
>                                   +2*log(sin(2))-log(2*cos(2)+2)
>                                   -log(2-2*cos(2))
>                                   +%i*atan(sin(1)/(cos(1)+1))
>                                   +%i*atan(sin(1)/(cos(1)-1))-**
> log(sin(1))
>                                   +log(2*cos(1)+2)/2+log(2-2***cos(1))/2
>                                   +%i*li[2](%e^(2*%i))+%i*li[2](**
> -%e^(2*%i))
>                                   -%i*li[2](%e^%i)-%i*li[2](-%e^**
> %i)+3*%i/2
> ------------------------------**---------------
> quadpack gives a numerical value -0.0455 for this integral,
> but maxima doesn't know how to get numbers for Li[2](z)
> if z is complex
>

Known problem.