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FindRoot and Bose-Einstein distribution
*To*: mathgroup at smc.vnet.net
*Subject*: [mg82738] FindRoot and Bose-Einstein distribution
*From*: P_ter <peter_van_summeren at yahoo.co.uk>
*Date*: Tue, 30 Oct 2007 03:27:39 -0500 (EST)
Hello,
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,
P_ter
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