summing a series in mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg64034] summing a series in mathematica
- From: Patrik <hosanagar at gmail.com>
- Date: Sat, 28 Jan 2006 02:23:48 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
I am trying to sum a function f(R) but want to specify an assumption for values one of the parameters can take. Specifically :
f = Q!/(R! (Q - R)!) (g ^ R) ((1 - g)^(Q - R)) (P(1 + 2 R d - P)/(1 + R d))
where g is a CDF and thus lies between 0 and 1. I wanted to get a simplified expression for Sum(f) where R goes from 1 to Q but want the system to account for the constraint on g. I tried:
FullSimplify[Sum[f,{R,Q}], {R, Q}], {g < 1, g > 0}]
But the simplification that mathematica gives has the following term in it:
Beta[g/g-1, 1/d + 1, Q]
Note that g/(g-1) is actually a negative number & the incomplete beta function is not defined for negative parameter. Is there a way to get Mathematica to realize that g<1 while making the simplification? Alternatively, is there a better way to simplify?
I tried replacing g/(1-g) by a new term 'x'. However, the resulting simplification had Beta[-x, 1+1/d, Q]. So, that didn't help. My ultimate goal is to take the derivative of the final expression (output of fullsimplify), so I don't mind an approximation if it makes the derivative look simple.
Your comments would be sincerely appreciated.