RSolve[a[n]==Sqrt[n]*a[Sqrt[n]]+n,a,n]

RSolve[j[n]==0.5*(1+Exp[i*n/2])*j[n/3],j,n]

NProduct[(2/(1+(E^((1/2) (3^(-n)) I)))),{n,1,-1-((Log[10])/(Log[3]))}]

NProduct[(2/(1+(E^((1/2) (3^(-n)) I)))),{n,1,IntegerPart[-1-((Log[1])/(Log[3]))],-1}]

IntegerPart[-1-((Log[10000])/(Log[3]))]

K[0]

N[K[1]]

EllipticK[0]

NProduct[n,{n,1,-4,-1}]

j[t_]:=NProduct[(2/(1+(E^((1/2) (3^(-n)) I)))),{n,1,IntegerPart[-1-((Log[t])/(Log[3]))],-1}];

j[1]

Plot[Abs[j[t]],{t,1,1000000000}]

Plot[Re[j[t]],{t,1,100000}]

Re[j[10]]

j[0]

RSolve[{j2[n]==0.5*(1+Exp[i*n/2])*j2[n/3],j2[0]==1},j2,n]

j2[t_]:=((NProduct[(2/(1+(E^((1/2) (3^(-n))*I)))),{n,1,IntegerPart[-1-((Log[t])/(Log[3]))],-1}])/(NProduct[(2/(1+(E^((1/2) (3^(-n))*I)))),{n,1,Infinity}]));

j2[0]

Plot[Re[j2[t]],{t,0,1000}]

j2[0]

Clear[j2]

j2[10]

Log[0]

LogLogPlot[Abs[Re[j2[t]]],{t,1,100000}]

Plot[Abs[j2[t]],{t,0,6}]

Plot[Abs[Re[j2[t]]],{t,0,1000000}]

LogLogPlot[Abs[Re[j2[t]]],{t,0,1000}]

LogLogPlot[Abs[Re[j2[t]]],{t,1,1000}]

Log[200]

N[Log[1000]]

Exp[2]

N[Exp[3]]

LogLogPlot[10^5,{x,1,100}]

RSolve[{j3[n]==0.5*(1+Exp[I*n/2])*j3[n/3],j3[0]==1},j3,n]

j3[t_]:=(0.9883254262165907 +0.12418816641187089* I) NProduct[(2/(1+(E^((1/2) I (3^(-K[1])))))),{K[1],1,-1-((Log[t])/(Log[3]))}];

j3[0]