# looking for numerical method to solve equation involving PolyLogs

Posted 8 years ago
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 I have this:VG = Table[i, {i, -30, 30, 0.1}] VG - (Vch +A* (-PolyLog[2, -E^-BVch] + PolyLog[2, -E^BVch]) ) == 0 A and B are constants. I'm trying to solve for Vch (another table). Any suggestions?thanks.
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Posted 8 years ago
 Daniel-Thanks for the quick reply. I have little Mathematica experience and so wanted to try to figure out how to carry out your suggestion before asking for further help. Sadly- still stuck. I reduced the size of my input table to simplify things. Am I just misunderstanding the syntax for FindFit? Here's what I get:In[15]:= VG = Table[i, {i, -30, -29, 0.1}]Out[15]= {-30., -29.9, -29.8, -29.7, -29.6, -29.5, -29.4, -29.3, -29.2, -29.1, -29.}In[16]:= FindFit[%, VG - (Vch + (-PolyLog[2, -E^-Vch] + PolyLog[2, -E^Vch])) == 0, Vch, VG]During evaluation of In[16]:= General::ivar: -30. is not a valid variable. >>Out[16]= FindFit[{-30., -29.9, -29.8, -29.7, -29.6, -29.5, -29.4, -29.3, -29.2, -29.1, -29.}, {-30. - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.9 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.8 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.7 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.6 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.5 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.4 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.3 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.2 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.1 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29. - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch]} == 0, Vch, {-30., -29.9, -29.8, -29.7, -29.6, -29.5, -29.4, -29.3, \ -29.2, -29.1, -29.}]
Posted 8 years ago
 Are you trying to solve for exact values, or get a best fit in terms of least squares? It looks like the latter since there are so many points. I'd suggest checking FindFit if that is in fact the case.