Forcing Trig Identities
- To: mathgroup at smc.vnet.net
- Subject: [mg94615] Forcing Trig Identities
- From: Gary McClelland <gary.mcclelland at colorado.edu>
- Date: Wed, 17 Dec 2008 06:36:36 -0500 (EST)
In earlier versions of Mathematica (I think 5 and before), the following code:
pmn[\[Rho]_ , x_, z_] :=
PDF[MultinormalDistribution[{0, 0}, {{1, \[Rho]}, {\[Rho], 1}}], {x,
z}]
Integrate[pmn[\[Rho], x, z], {x, -Infinity, 0}, {z, -Infinity, 0},
Assumptions -> {\[Rho] ^2 < 1, \[Rho] > 0}]
yielded:
(\[Pi] + 2 ArcSin[\[Rho]])/(4 \[Pi])
now (Mathematica 7), I get the mathematically equivalent but less desirable:
(\[Pi] - ArcTan[Sqrt[-1 + 1/\[Rho]^2]])/(2 \[Pi])
TrigReduce and FullSimplify fail to simplify what Mathematica 7 gives to the simpler expression Mathematica 5 yielded. any suggestions on how to force trig identities?
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