(integer n) as a 𝜗 constant, I worked all morning. Out[1208]= EllipticTheta[1, 1/4 (2 n - 1) \[Pi], q] == ((-1)^(7/8) I^(n (1 + n)) EllipticTheta[2, 0, I q])/Sqrt[2] Try it: In[1209]:= Table[% /. q -> 1/2, {n, 4}] Out[1209]= {EllipticTheta[1, \[Pi]/4, 1/ 2] == -(((-1)^(7/8) EllipticTheta[2, 0, I/2])/Sqrt[2]), EllipticTheta[1, (3 \[Pi])/4, 1/ 2] == -(((-1)^(7/8) EllipticTheta[2, 0, I/2])/Sqrt[2]), EllipticTheta[1, (5 \[Pi])/4, 1/2] == ((-1)^(7/8) EllipticTheta[2, 0, I/2])/Sqrt[2], EllipticTheta[1, (7 \[Pi])/4, 1/2] == ((-1)^(7/8) EllipticTheta[2, 0, I/2])/Sqrt[2]} Mma knows squat about 𝜗. Try numbers. In[1229]:= N[%1209] Out[1229]= {False, False, False, False} AARRGGHH!! Maybe it's just a sign or something easy to fix. Change equations to lists: In[1211]:= N[%% /. Equal -> List] Out[1211]= {{0.873615, 0.873615 - 1.11022*10^-16 I}, {0.873615, 0.873615 - 1.11022*10^-16 I}, {-0.873615, -0.873615 + 1.11022*10^-16 I}, {-0.873615, -0.873615 + 1.11022*10^-16 I}} In[1230]:= Chop[%1211] Out[1230]= {{0.873615, 0.873615}, {0.873615, 0.873615}, {-0.873615, -0.873615}, {-0.873615, -0.873615}} In[1231]:= Equal @@ # & /@ % Out[1231]= {True, True, True, True} AARRGGHH!! I was right all along! Braindead Mathematica introduced spurious imaginary errors, and then screamed False before it would have been possible to Chop them! --rwg