rwg> Ironically, http://functions.wolfram.com/EllipticFunctions/WeierstrassP/16/ has the multiple and half "angle" formulæ, so FunctionExpand should evaluate the explicit general formula exactly, possibly providing nicer recurrences than I have given here.<rwg For starters, the double "angle" formula, for general congruent # n, gives this amazingly simple x2 = Out[1115]= (n^2 + x1^4)/(2 x1 Sqrt[x1^4 - n^2]) In[1116]:= % /. n -> 5 /. x1 -> 5/2 Out[1116]= 41/12 There was a time when some of us wondered if this was the only solution to x^2±5 = ⃞. In[1117]:= %1115 /. n -> 5 /. x1 -> % Out[1117]= 3344161/1494696 Here go n = 6 and 7: In[1118]:= %1115 /. n -> 6 /. x1 -> 5/2 Out[1118]= 1201/140 In[1119]:= %1115 /. n -> 6 /. x1 -> % Out[1119]= 2094350404801/483435791720 In[1120]:= Sqrt[%^2 + {6, -6}] Out[1120]= {2405943600001/483435791720, 1727438169601/483435791720} In[1121]:= %1115 /. n -> 7 /. x1 -> 5 Out[1121]= 337/120 rwg> Maybe even elementary closed forms.<rwg Well, simple as it is, I don't expect to see anyone writing the nth iterate of %1115. --rwg