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Re: Evaluating Exponential functions

• To: mathgroup at smc.vnet.net
• Subject: [mg125952] Re: Evaluating Exponential functions
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Mon, 9 Apr 2012 05:33:57 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jlmfak$mhr$1@smc.vnet.net>

On 06/04/2012 11:08, leigh pascoe wrote:
> 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
>

You have missed out the _ characters in the definition of inc3 - so it 
doesn't match anything useful. You need:

inc3[x_, M_, \[Tau]_, \[Phi]_, \[Tau]2_] .....

David Bailey
http://www.dbaileyconsultancy.co.uk