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 > > 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 > ____________________________________ > >