Groups > comp.soft-sys.math.mathematica > #3115

[Mathematica8,solve] saddlepoint approx, solving a sum

From	gideonmath <g.s.j.cramwinckel@students.uu.nl>
Newsgroups	comp.soft-sys.math.mathematica
Subject	[Mathematica8,solve] saddlepoint approx, solving a sum
Date	2011-06-16 08:00 +0000
Organization	Steven M. Christensen and Associates, Inc and MathTensor, Inc.
Message-ID	<itcd6t$csa$1@smc.vnet.net> (permalink)

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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?

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[Mathematica8,solve] saddlepoint approx, solving a sum gideonmath <g.s.j.cramwinckel@students.uu.nl> - 2011-06-16 08:00 +0000

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