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MathGroup Archive 2007

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Re: Help with plotting and iterations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72829] Re: Help with plotting and iterations
  • From: "ashesh" <ashesh.cb at gmail.com>
  • Date: Sun, 21 Jan 2007 06:05:54 -0500 (EST)
  • References: <eoshbr$9er$1@smc.vnet.net>

I got a reply to the above problem by Bob and it works excellently...
Here is the solution:

result[p_]:=Module[{a=1/2,b=1/4,h=1/4,
       m,m1,z,t,t1,t2,b1,c,x,aa,bb},
     m=b/a;
     m1=Sqrt[1-m^2];
     z=(p-I*h);
     t=ArcSin[z];
     t1=Re[t];
     t2=-Im[t];
     b1=Cot[t1]^2+m^2*Sinh[t2]-m1;
     c=m1^2*Cot[t1]^2;
     x=Reduce[{x^2 - b1*x - c==0,x>=0},x]//
           Last//N;
     aa=ArcCot[Sqrt[x]];
     bb=ArcTan[Sqrt[x/m1]];
     {EllipticF[aa,m],EllipticF[bb,m1]}];

TableForm[Join[
   Table[Prepend[result[p],p],{p,0.01,0.99,0.01}],
   Table[Prepend[result[p],p],{p,1,10}]],
 TableHeadings->{None,{"p","Faa","Fbb"}}]

ParametricPlot[result[p], {p, 0.01, Pi},
   AxesLabel->{"Faa","Fbb"},ImageSize->432];

Regards.
Ashesh


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