Out[157]= Im[dragun[EllipticTheta[3, 0, 1/4] - 1]] == 1/2 (EllipticTheta[3, 0, 1/2] - 1) In[159]:= N[%157 /.EllipticTheta[3, 0, q_] :> Round[EllipticTheta[3, 0, q], 2^-691], 99] Out[159]= 0.564468413605938579334729274272475662306258269970439046444505596028480133179578406659130640162469148 == 0.564468413605938579334729274272475662306258269970439046444505596028480133179578406659130640162469148 Out[139]= EllipticTheta[3, 0, 1/2]/2 - Im[dragun[EllipticTheta[3, 0, 1/4]/2]] + Re[dragun[EllipticTheta[3, 0, 1/4]/2]] == 3/2 In[146]:= $RecursionLimit = 5333; N[%139[[1]] /. T : EllipticTheta[3, 0, _] :> Round[T, 2^-999], 99] Out[146]= 1.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 —rwg NonMathematickers should wonder why I goosed $RecursionLimit simply to replace the 𝜗₃ by a rational approximation. The recursion is in the definition of dragun, iff it receives a rational argument. So its definition begins dragun@0 = 0; dragun@1 = 1; dragun[t_Real | t_Rational] := piecewiserecursivefractal[ . . .