MathGroup Archive 2007

[Date Index] [Thread Index] [Author Index]

Search the Archive

FindRoot and Bose-Einstein distribution

  • To: mathgroup at
  • Subject: [mg82738] FindRoot and Bose-Einstein distribution
  • From: P_ter <peter_van_summeren at>
  • Date: Tue, 30 Oct 2007 03:27:39 -0500 (EST)

I have two functions and two values:
Clear[p, q, k, mm, mn]
n[p_, q_] := Sum[k/(Exp[p + k q ] - 1), {k, 1, 10000}]
m[p_, q_] := Sum[1/(Exp[p + k q ] - 1), {k, 1, Infinity}]
mm = 0.501
mn = 41.0959
The first two equations are the Bose-Einstein distribution. Given mm and mn, find p and q. 
A first estimation is: p=5.086,q= 0.01226
I know that n[p_,q_] is stable until k = 50000 for p=5.086 and q= 0.01226. My check is: n[5.086,0.01226]= 41.1969 
m[p_,q_] is also stable until 100000 and m[5.086,0.01226]= 0.502762
Everything seems ok.
So, I tried:
FindRoot[{m[p, q] - mm, n[p, q] - mn}, {{p, 5}, {q, 0.1}}]
The answer from FindRoot is that the Sum does not converge.
What did I do wrong, what went wrong, why?
with friendly greetings,

  • Prev by Date: Re: A riddle: Functions that return unevaluated when they cannot
  • Next by Date: Re: Show and scaling
  • Previous by thread: Re: Setting Negatives to Zero
  • Next by thread: Re: FindRoot and Bose-Einstein distribution