acx01bc . on Fri, 14 Jul 2017 13:25:17 +0200


[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]

(Jacobi) theta function

Hi,  you should mention in https://pari.math.u-bordeaux.fr/dochtml/html/Transcendental_functions.html that the usual 

       vartheta(x) = sum_n    exp(-Pi*x*n^2) 

function is obtained from

        vartheta(x) = exp(-Pi*x/4)*theta(exp(-Pi*x),Pi/2+ Pi*x/(2*I))


a sanity check for the modularity

     \p 50
      x = 0.2;
      a = vartheta(x);
      b = x^(-1/2)*vartheta(1/x);
      abs(a - b) < 1E-50