Re: derivative of a well-behaved function
- To: mathgroup at smc.vnet.net
- Subject: [mg99520] Re: derivative of a well-behaved function
- From: dh <dh at metrohm.com>
- Date: Thu, 7 May 2009 06:34:34 -0400 (EDT)
- References: <gtrl0i$1mf$1@smc.vnet.net>
Hi Ricardo,
I can not tell what is going wrong. But you could calcuölate an
approximate function and get the derivative of it. Herei is your example:
==================================
fun = FunctionInterpolation[ZS[z, 1, 0.5], {z, -4, 4}];
Plot[{fun[z], ZS[z, 1, 0.5]}, {z, -4, 4}]
Plot[fun'[z], {z, -4, 4}]
=================================
Daniel
Ricardo Samad wrote:
> Dear all,
>
> the following ZS function is an analytical description of the transmittance
> of a laser beam through an Iris after propagating inside a nonlinear sample
> (Z-Scan curve):
>
> \[Gamma][z_, z0_] := 1/2 (I/z0 (z + (z^2 + z0^2)/(DD - z)) + 1);
>
> ZS[z_, z0_, \[Phi]_] :=
> Abs[\[Gamma][z, z0] Gamma[\[Gamma][z, z0], 0,
> I \[Phi]/(1 + (z/z0)^2)] /(I \[Phi]/(1 + (z/z0)^2))^\[Gamma][z,
> z0]]^2;
>
> Altough the function has imaginary arguments and is defined in terms of the
> incomplete Gamma function, it is well-behaved and Mathematica calculates an=
> d
> plots it without problems:
>
> DD = 300;
> Plot[ZS[z, 1, 0.5], {z, -4, 4}]
>
> The problem is that when I calculate its derivative in z, the result is
> given in terms of infinite quantities and DirectInfinity functions, and it
> is not possible to get numerical values of it neither plot its graph:
>
> dZS = D[ZS[z, 1, 0.5], z];
> dZS /. z -> 1
> N[%]
> Plot[dZS[z, 1, 0.5], {z, -4, 4}]
>
> Since the ZS function is well-behaved and has no discontinuities, its
> derivative should be easily evaluated to numerical values and also plotted.
> Does anybody has any idea on how to obtain the values? (I could easily writ=
> e
> a function to numerically calculate the derivative, but that=B4s not really
> what I want).
>
> Thank you,
>
> Ricardo
>
>
> --
> ____________________________________
> Ricardo Elgul Samad
>
> tel: (+55 11) 3133-9372
> fax: (+55 11) 3133-9374
>
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