1
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When I run the code,

ClearAll["Global`*"]

G = 0.01;
β = 1;
ωc = 50;

integralgamma[ω_, τ_] :=  4 G ω Exp[-ω/ωc] ((1 - Cos[ω τ])/ω^(2)) Coth[β ω/2];

mem : γ[τ_?NumericQ] :=  
  mem = NIntegrate[integralgamma[ω, τ], {ω, 0, Infinity}, 
  MaxRecursion -> 15, PrecisionGoal -> 5, WorkingPrecision -> 15];

oldprob[nx_, ny_, nz_, τ_] := 1/2 (1 + nz^2 + Exp[-γ[τ] ]*(nx^2 + ny^2));

newprob[nx_, ny_, nz_, τ_] := 1/2 (1 + Sqrt[nz^2 + Exp[-γ[τ] ]^2 * (nx^2 + ny^2) ]);

Plot[
  {oldprob[1/Sqrt (2), 1/Sqrt (2), 0, τ], 
   newprob[1/Sqrt (2), 1/Sqrt (2), 0, τ]}, 
  {τ, 0, 2}, 
  PlotRange -> {0, 1}, MaxRecursion -> 10, WorkingPrecision -> 15],

I get the error:

NIntegrate::inumr: The integrand integralgamma has evaluated to non-numerical values for all sampling points in the region with boundaries {{∞, 0.}}.

What could be the issue?

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closed as off-topic by george2079, m_goldberg, Wjx, Michael E2, Bob Hanlon Aug 13 '16 at 13:49

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – george2079, m_goldberg, Wjx, Michael E2, Bob Hanlon
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 1
    $\begingroup$ Change in Plot code : Sqrt (2) to Sqrt[2] $\endgroup$ – Mariusz Iwaniuk Aug 12 '16 at 15:52
2
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From Mathematica Documentation Center:

It is important to remember that all function arguments in the Wolfram Language are enclosed in square brackets, not parentheses. Parentheses in the Wolfram Language are used only to indicate the grouping of terms, and never to give function arguments.

ClearAll["Global`*"]

G = 0.01;
β = 1;
ωc = 50;

integralgamma[ω_, τ_] :=  4 G ω Exp[-ω/ωc] ((1 - Cos[ω τ])/ω^(2)) Coth[β ω/2];

mem : γ[τ_?NumericQ] :=  mem = NIntegrate[
  integralgamma[ω, τ], {ω, 0, Infinity}, 
   MaxRecursion -> 15, PrecisionGoal -> 5, WorkingPrecision -> 15];

oldprob[nx_, ny_, nz_, τ_] := 1/2 (1 + nz^2 + Exp[-γ[τ] ]*(nx^2 + ny^2));

newprob[nx_, ny_, nz_, τ_] := 1/2 (1 + Sqrt[nz^2 + Exp[-γ[τ] ]^2 * (nx^2 + ny^2) ]);

Plot[{oldprob[1/Sqrt[2], 1/Sqrt[2], 0, τ], 
 newprob[1/Sqrt[2], 1/Sqrt[2], 0, τ]}, {τ, 0, 2}, 
  PlotRange -> {0, 1}, MaxRecursion -> 10, WorkingPrecision -> 15]

enter image description here

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