       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 = With[{sigma = Sqrt, 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

From: tatsec [mailto:markelbbs at tom.com]

The program is :

dotnum=40;
sigma=Sqrt;
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

```

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