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Pattern Matching for Exponentials


I am looking for a pattern-matching replacement rule which will 
transform exponential functions of the form exp(n i t) into 
(1/(n^2-1))exp(n i t) where i = sqrt[-1]. For example, exp(2 i t) 
should convert to (1/3)exp(2 i t). I've tried the following code without 
success :

In:     Exp[2 i t]   /.  Exp[n_ i t] -> Exp[n i t]/(n^2-1)

Out:  e^2 i t

I would appreciate any suggestions as to how this code should be 
modified.

Thanks,

Rick Eller


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