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Evaluating Exponential functions
Posted:
Apr 6, 2012 6:08 AM


Dear Experts,
I am working with an age specific risk function
inc1[x_, M_, \[Tau]_, \[Phi]_] := M/\[Tau] \[Phi]^M E^((x/\[Tau])) (1  E^((x/\[Tau])))^(M  1)
where x is the age and M, tau and Phi are constants. This function plots, can be integrated numerically and Manipulated easily in Mathematica.
I am also interested in the slightly more complicated function
inc3[x, M, \[Tau], \[Phi], \[Tau]2] := ( E^((x/\[Tau])) (1  E^((x/\[Tau])))^(2 + M) (1  E^((x/\[Tau]2))) (1 + M) \[Phi]^M)/\[Tau] + ( E^((x/\[Tau]2)) (1  E^((x/\[Tau])))^(1 + M) \[Phi]^M)/\[Tau]2
This function has an additional parameter tau2. When tau2==tau the two functions should be identical. However the second function will not Plot, Integrate or be Manipulated in Mathematica. In fact it will not even evaluate for specific values of the parameters. e.g.
In[10]:= inc1[10, 12, 8, .65] inc3[10, 12, 8, .65, 8]
Out[10]= 0.0000596328
Out[11]= inc3[10, 12, 8, 0.65, 8]
The output for the two functions should be identical. What am I not understanding here? How can I define this function so that I can numerically integrate it and Plot its values over a range of x.
Thanks for any suggestions.
LP



