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Evaluating Exponential functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125915] Evaluating Exponential functions
  • From: leigh pascoe <leigh at evry.inserm.fr>
  • Date: Fri, 6 Apr 2012 06:02:37 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

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



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