derivative of a well-behaved function

*To*: mathgroup at smc.vnet.net*Subject*: [mg99466] derivative of a well-behaved function*From*: Ricardo Samad <resamad at gmail.com>*Date*: Wed, 6 May 2009 05:24:52 -0400 (EDT)

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 Centro de Lasers e Aplica=E7=F5es IPEN/CNEN-SP AV. Prof. Lineu Prestes 2242 Cidade Universit=E1ria 05508-000 S=E3o Paulo - SP Brazil ____________________________________

**Follow-Ups**:**Re: derivative of a well-behaved function***From:*Daniel Lichtblau <danl@wolfram.com>