Bug introduced in 9.0 and fixed in 10.0.0
In Mathematica 8 the following expression evaluates and returns a result in terms of InverseFunction
:
NSolve[Integrate[x^(1/2)/(Exp[x - μ] - 1), {x, 0, ∞}] == C, μ]
where C
is a constant. But in Mathematica 9 the expression does not evaluate:
NSolve::nsmet: This system cannot be solved with the methods available to NSolve. >>
Is this a bug, a regression, or a feature? And how can this equation can be solved in V9?
Particular, trying to solve this:
NSolve[PolyLog[3/2, 20 x] == 2, x]
In Mathematica 8 and Mathematica 9 gives different results:
Mathematica 8 (correct result):
NSolve::ifun: Inverse functions are being used by NSolve, so some solutions may not be found; use Reduce for complete solution information. >>
{{x -> 0.05 InverseFunction[PolyLog, 2, 2][3/2,
2.0000000000000000000000000000000]}}
NSolve::nsmet: This system cannot be solved with the methods available to NSolve. >>
NSolve[PolyLog[3/2, 20 x] == 2, x]
UPD: That's a confirmed bug with NSolve
, that I already reported to developers of Wolfram Mathematica long time ago.
eqn = Integrate[x^(1/2)/( Exp[x - \[Mu]] - 1), {x, 0, Infinity}]
it looks likeeqn
is always positive so the equation has no solution. $\endgroup$==
sign. $\endgroup$Root
instead ofInverseFunction
). $\endgroup$