Mathematica Stack Exchange is a question and answer site for users of Mathematica. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I cannot plot this function as I am getting errors. I am not sure what I am doing wrong.

Seems to work when $$n \rightarrow 1,$$ but when $$n \rightarrow 2,$$ I get a whole bunch of errors and nothing is plotted.

Here is the code:

$$ \text{Plot}\left[\frac{n e^{-t (\lambda +\mu )} I_1\left(2 t \sqrt{\lambda \mu }\right) \left(\int_0^t \frac{e^{t (-\lambda -\mu )} I_1\left(2 t \sqrt{\lambda \mu }\right)}{\sqrt{\rho } t} \, dt\right){}^{n-1}}{\sqrt{\rho } t}\text{/.}\, \left\{\lambda \to 0.99,\mu \to 1,\rho \to \frac{1}{2},n\to \{2\}\right\},\{t,0,10\},\text{PlotRange}\to \text{All}\right]$$

Here is copyable code:

Plot[(n*BesselI[1, 2*t*Sqrt[λ*μ]]*            
      Integrate[(E^(t*(-λ - μ))*
           BesselI[1, 2*t*Sqrt[λ*μ]])/(t*Sqrt[ρ]), 
                {t, 0, t}]^(-1 + n))/
    E^(t*(λ + μ))/(t*Sqrt[ρ]) /. 
     {λ -> 0.99, μ -> 1, ρ -> 1/2, n -> {2}}, {t, 0., 10}, PlotRange -> All]
share|improve this question
Can you post copyable Mathematica code please? – Szabolcs Feb 27 '14 at 3:56
I don't know how to do that. Could you explain how? – Pierre M Fiorini Feb 27 '14 at 3:59
That's good enough, thank you. I cleaned up the formatting of the code slightly for readability. You can select the code and use Edit -> Copy As -> Input Text. Then when you paste it here, select it again and press the code button in the toolbar to format it. – Szabolcs Feb 27 '14 at 4:07
fyi, I get errors !Mathematica graphics – Nasser Feb 27 '14 at 4:08
I get those same errors too. I was hoping there could be a workaround. It works for $$n \rightarrow 1,$$ but when $$n > 1,$$ I get those errors. – Pierre M Fiorini Feb 27 '14 at 4:14
up vote 0 down vote accepted
fun[t_, n_, \[Rho]_, \[Lambda]_, \[Mu]_] := (n*
     BesselI[1, 2*t*Sqrt[\[Lambda]*\[Mu]]]*
     NIntegrate[(E^(s*(-\[Lambda] - \[Mu]))*
          BesselI[1, 2*s*Sqrt[\[Lambda]*\[Mu]]])/(s*Sqrt[\[Rho]]), {s,
         0, t}]^(-1 + n))/E^(t*(\[Lambda] + \[Mu]))/(t*Sqrt[\[Rho]])


 Plot[fun[t, j, 1/2, 0.99, 1], {t, 0, 10}, 
  PlotRange -> {0, 1}], {{j, 0.5, "n"}, 0.5, 2.5, 
  Appearance -> "Labeled"}]

enter image description here

share|improve this answer
Thanks for your help - Much appreciated. – Pierre M Fiorini Feb 27 '14 at 18:23

Is this how the function supposed to look like?

 int[t1_, lam_, mu_, rao_] := NIntegrate[(E^(t*(-lam - mu))*
      BesselI[1, 2*t*Sqrt[lam*mu]])/(t*Sqrt[rao]), {t, 0, t1}];

f[t_, {lam_, mu_, rao_, n_}] := (n*BesselI[1, 2*t*Sqrt[lam*mu]]*
   int[t, lam, mu, rao]^(-1 + n))/E^(t*(lam + mu))/(t*Sqrt[rao]);

parm = {lam -> 0.99, mu -> 1, rao -> 1/2, n -> 2};
Plot[f[t, {lam, mu, rao, n} /. parm], {t, 0, 10}, PlotRange -> All, 
   Frame -> True, GridLines -> Automatic,  GridLinesStyle -> LightGray]

Mathematica graphics

share|improve this answer
I am not sure. I'm still researching this. – Pierre M Fiorini Feb 27 '14 at 16:53

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.