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In[1561:= tit_, v_] := Sqrt[-Sin[2 t] / Ta.[Piv/ 2] + SqrtESin[2 t] ^2 /Tan[Piv / 2] ^2 + l]]
In[157]:= r[t, v]
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In[173}:= pl = PolarPlot[{r[t, i] , r[t, .8], r[t, .6], r[t, .4], r[t, .2]},
{%, 0, Pi/2}, PlotStyle ÿBlue];
p2 = PolarPlo%[{r[t, -l] , r[t, -.8], tit, -.6], r[t, -.4], r[t, -.2]},
{t, Pi/ 2, Pi}, PlotStyle ÿ Red];
p3 = PolarPlot[{r[t, 1] , r[%, .8], r[t, .6], r[t, .4], r[t, .2]},
{t, Pi, 3 Pi/2}, PlotStyle ÿ Blue];
p4 = PolarPlo%[{r[t, -i] , r[t, -.8], r[t, -.6], r[t, -.4], r[t, -.2]},
{t, 3Pi/2, 2 Pi}, PlotStyle ÿ Red] ;
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In[1ÿ]:= Sum[Sum[4 ((-l)^n -I) ((-i)^m -i) Sin[nPi/ 2] Sin[mPi/2] 2 Sinh[PiSqrt[n^2 +m^2] /2] /
(Pi^2 nmSinh[PiSqrtEn^2 +m^2]]), {n, i, i00}], {m, i, i00}] // N
Out[183]= 0.333333
rn[184]:= Sum[Sum[4 ((-i)^n -1) ((-I)^m -I) Sin[nPi/2] SinEmPi/2] 2 Sinh[PiSqrt[nÿ2 +m^2] /2] /
(Pi^2nmSinhEPiSqrt[n^2+m^2]]), {n, 1, i}], {m, i, I}] // N
Out[184]= 0.347546
In[186]:= Sum[Sum[4 ((-i)^n -1) ((-1)^m -1) Sin[nPi/2] Sin[mPi/2] 2 Sinh[PiSqrt[n^2 +m^2] /2] /
(Pi^2nmSinh[PiSqrt[n^2+mÿ2]]), {n, i, 3}], {m, 1, 3}] // N
u1{1861= 0.332958
In[187]:= Sum[Sum[4 ((-1)^n -1) ((-1)ÿm -I) Sin[nPi/2] Sin[mPi/2] 2 Sinh[PiSqr%[nA2 ÷m^2] /2] /
(Piÿ2 nmSinh[PiSqrt[n^2 +m^2] ]) , {n, I, 5}] , {m, i, 5}] // N
0ut[187]= 0.333345
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