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Re: Keep it real

On 30 Nov, 10:04, Sam Takoy <sam.ta... at> 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[1] MathieuC[-((a^2 \[Lambda])/2), (a^2 \[Lambda])/4,
       1/2 I (H/a - (2 z)/a)] -
     C[2] 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

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

Out[1]= -2.65844*10^7 + 0. I

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

Out[1]= 0. + 2.65844*10^7 I

So if C[1] is chosen real and C[2] 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
for more information about the Mathieu functions.

Best regards

Ingolf Dahl
ingolf.dahl at

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