I need to solve an equation of this form:
NSolve[a + x^b + PolyLog[c, x] + PolyLog[d, 1/x] == 0, x]
Where $a, b, c, d$ are constants.
For the sake of simplicity we can make $a = b = c = d$. Ok I know that with no chosen variables, the question is basically impossible but besides that, what I would like to get is a sort of plot in function of those constant, in a range let's say from $-3$ to $+5$ each one.
But then another problem would arise: having the plot, let's say for $a = b = c = d = 2$, how can I ask Mathematica to give me the numerical solution of the above equation? Solve seems not working!
(WM 10.0.2.0)
FindRoot
. $\endgroup$In[433]:= NSolve[ 2 + x^2 + PolyLog[2, x] + PolyLog[2, 1/x] == 0 && -100 < x < 100, x] Out[433]= {{x -> -0.370672770423}}
$\endgroup$In[438]:= NSolve[ 2 + x^2 + PolyLog[2, x] + PolyLog[2, 1/x] == 0 && -100 <= Re[x] <= 100 && 1 <= Im[x] <= 200, x] Out[438]= {{x -> -0.1147574412 + 1.19969565036 I}}
$\endgroup$