RootSearch issue

• To: mathgroup at smc.vnet.net
• Subject: [mg112694] RootSearch issue
• From: "becko" <becko565 at hotmail.com>
• Date: Mon, 27 Sep 2010 05:47:03 -0400 (EDT)

```Hi. This is an strange issue I'm having with v1.4 of Ersek's RootSearch
package. I'm looking for the roots of a function and it so happens that
if I specify a small interval, it finds the roots, but when I increase
the interval, it doesn't find any root!. Specifically, here's a code
sample:

In[39]:= \[Gamma]even[r_, k_, e_] :=
I MathieuCPrime[MathieuCharacteristicA[r, k^2/4], k^2/4,
I ArcTanh[Sqrt[1 - e^2]]];
rootsEven[r_, e_, {kmin_, kmax_}, opts : OptionsPattern[]] :=
RootSearch[\[Gamma]even[r, k, e] == 0, {k, kmin, kmax}, opts] // Quiet

In[38]:= rootsEven[4, 5/20, {0, 10}][[All, 1, 2]]

Out[38]= {1.35064, 2.3571, 3.21912}

In[36]:= rootsEven[4, 5/20, {0, 100}][[All, 1, 2]]

Out[36]= {1.35064, 2.3571, 3.21912}

In[35]:= rootsEven[4, 5/20, {0, 1000}][[All, 1, 2]]

Out[35]= {}

Is there an explanation for this? Thanks.

```

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