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[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 look: 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 http://mathworld.wolfram.com/MathieuFunction.html for more information about the Mathieu functions. Best regards Ingolf Dahl ingolf.dahl at telia.com