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How can I get the output expressed in terms of p1 and p2 instead of exponentials?

gau[x_, v_] := Exp[-(x^2)/(2*v)]/Sqrt[2*Pi*v];
p1[x_] := gau[x - m, B + v]/2 + gau[x + m, B + v]/2;
p2[x_] := gau[x - m, B + v]/2 - gau[x + m, B + v]/2;
Simplify[D[Log[p1[x]], {v, 3}]]

I want to substitute:

Exp[(x+m)^2/(2*(B+v))]/2 + Exp[(x-m)^2/(2*(B+v))]/2 -> p1
Exp[(x+m)^2/(2*(B+v))]/2 - Exp[(x-m)^2/(2*(B+v))]/2 -> p2

but obvious that doesn't work.

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closed as unclear what you're asking by Dr. belisarius, MarcoB, bbgodfrey, Jens, dr.blochwave Jun 3 '15 at 7:56

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    $\begingroup$ Probable duplicate: (3822) (Still not answered to my full satisfaction.) $\endgroup$ – Mr.Wizard Jun 3 '15 at 4:31

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