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Question: how to express a complicated function of t in terms of another function in maple

Question:how to express a complicated function of t in terms of another function in maple

litun 95
student taylor
November 04 2013
3

I have  

a(t):= (0.4292960410)*(t^3+20.0*t^2+105.0*t+138.0)^5/((t+1.881246817-0.5978370144*I)*(t+2.472494183-0.1946676251*I)*(t+5.550661347)*(t+5.496908401)*(t+12.46933729)*(t+12.44618893-0.9642646277e-2*I)*(t+0.5725282710)*(t+5.589440415)*(t+12.49222265)*(t+12.44618893)*(t+12.46933729)*(t+5.496908401)*(t+5.550661347)*(t+2.472494183+0.1946676251*I)*(t+1.881246817+0.5978370144*I))

 

b(t)=(1.8*t^2+34.1*t+138.)/(t^3+20.*t^2+105.*t+138.)

 

and 

 

F(t):={0.5738910678*a(t)*[1-b(t)]}/t*0.5137681159

I have expanded F(t) in series form using taylor series expansion formula in terms of t.

My question is 

                           Can it be expanded in series form in terms of b(t).
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