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[Mathematica8,solve] saddlepoint approx, solving a sum

• To: mathgroup at smc.vnet.net
• Subject: [mg119649] [Mathematica8,solve] saddlepoint approx, solving a sum
• From: gideonmath <g.s.j.cramwinckel at students.uu.nl>
• Date: Thu, 16 Jun 2011 04:00:10 -0400 (EDT)

For a saddlepoint approximation i need to solve the following equation:
K'[t]==y^*,t 

K[t_]:= Sum[Log[1-p[i]+p[i]Exp[c[i]t]], {i,1,n}]
where p[i] denotes a probability (hence all p[i] in (0,1) and \sum p_i=1. Same holds for the c[i], but c[i], p[i] all independent.

Solve works for a 1-term Sum, but for 2 or more terms I get this error:
Solve::nsmet: This system cannot be solved with the methods available to Solve. >>

Why does the method fail? I suppose that it has to do something with the log[..+...] kind of terms. 
IS there a workaround?

• Follow-Ups:
  • Re: saddlepoint approx, solving a sum
    • From: DrMajorBob <btreat1@austin.rr.com>