Abstract:
We obtain two closed-form nonrecurrent formulas for the coefficients of the
Taylor series of the Weierstrass sigma function related to elliptic function
theory.
There results are derived from the differential-recurrence and
two-dimensional recurrence relations that arise when searching for the analytic
solutions of the system of partial differential equations constructed by
Weierstrass for the sigma function.
Keywords:elliptic function theory, Weierstrass sigma function, two-dimensional
recurrence relations.
