       Re: Keep it real

• To: mathgroup at smc.vnet.net
• Subject: [mg114389] Re: Keep it real
• From: Ingolf Dahl <ingolf.dahl at gmail.com>
• Date: Fri, 3 Dec 2010 05:19:03 -0500 (EST)
• References: <id2en6\$d8l\$1@smc.vnet.net>

```On 30 Nov, 10:04, Sam Takoy <sam.ta... at yahoo.com> wrote:
> Hi,
>
> Is there a way to make Mathematica stick to real numbers and functions
> as much as possible? For example, could I somehow get two real function
> solutions to the problem
>
> DSolve[g''[z] + (\[Lambda] Cosh[(z - H/2)/a]^2) g[z] == 0, g, z];
>
> Many thanks in advance,
>
> Sam

Have you checked if the solution is real or complex? I obtain the
following solution

{{g -> Function[{z},
C MathieuC[-((a^2 \[Lambda])/2), (a^2 \[Lambda])/4,
1/2 I (H/a - (2 z)/a)] -
C MathieuS[-((a^2 \[Lambda])/2), (a^2 \[Lambda])/4,
1/2 I (H/a - (2 z)/a)]]}}

The third arguments of MathieusC and MathieusS are imaginary, but
look:

In:= MathieuC[2, 1, 3.2 I]

Out= -2.65844*10^7 + 0. I

In:= MathieuS[2, 1, 3.2*I]

Out= 0. + 2.65844*10^7 I

So if C is chosen real and C imaginary, there is a good chance
that you get a real value out. I have not checked for all values of
the parameters.

Please also look up http://mathworld.wolfram.com/MathieuFunction.html
for more information about the Mathieu functions.

Best regards

Ingolf Dahl
ingolf.dahl at telia.com

```

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