A symbolic decision procedure for relations arising among Taylor coefficients of classical Jacobi theta functions

摘要

The class of objects we consider are algebraic relations between the four kinds of classical Jacobi theta functions theta(j)(z vertical bar r), j = 1,, 4, and their derivatives. We present an algorithm to prove such relations automatically where the function argument z is zero, but where the parameter tau. in the upper half complex plane is arbitrary. (C) 2017 Elsevier Ltd. All rights reserved.