RE: Using FindRoot in complex funtion

*To*: mathgroup at smc.vnet.net*Subject*: [mg71936] RE: [mg71900] Using FindRoot in complex funtion*From*: "David Park" <djmp at earthlink.net>*Date*: Mon, 4 Dec 2006 06:39:31 -0500 (EST)

Raymond, Do you mean Pi instead of pi? Why don't you try evaluating the integral for some L cases before you plug it into FindRoot? When I tried to evaluate some of the integrals, they didn't converge because of the singularity at zero. f[2] = With[{sigma = Sqrt[2], L = 2}, Integrate[ 2^(1/2 - L/2)*sigma^(-1 - L)*(Abs[t])^(1/2*(-1 - L))* BesselK[(1 - L)/2, Abs[t]/sigma]/(Sqrt[Pi]*Gamma[L/2]), {t, 0, y}]] with the error message... \!\(Integrate::"\<idiv\>" : \*"\"\<Integral of \ \!\(\[ExponentialE]\^\(-\(Abs[t]\/\@2\)\)\/Abs[t]\^2\) does not converge on {\ \!\(0, y\)}.\>\""\) David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: tatsec [mailto:markelbbs at tom.com] The program is : dotnum=40; sigma=Sqrt[2]; For[L=2,L<=dotnum,L=L+2, FindRoot[Integrate[2^(1/2-L/2)*sigma^(-1-L)*(Abs[t])^(1/2*(-1-L))*BesselK[(1 -L)/2,Abs[t]/sigma]/(Sqrt[pi]*Gamma[L/2]),{t,0,y}],{y,1}];] when L<30, FindRoot can find the root of function.but L=>30,FindRoot can't calculation.So How to solve this problem? Thanks in advance for any help you can give me. Raymond