A rational approximation to Weierstrass’ 𝑃-function

Abstract

A rational approximation to Weierstrass’ ℘ \wp -function in the equianharmonic case for unit period parallelogram is given. With a third-degree numerator polynomial and a fourth-degree denominator polynomial the maximal error for | z | > 1 / 3 |z| > 1/\sqrt 3 becomes 3 ⋅ 10 − 14 3 \cdot {10^{ - 14}} . The approximation of ℘ ( z ) \wp (z) is then used to calculate a rational approximation to ℘ ′ ( z ) \wp ’(z) together with an error bound.