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