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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

A rational approximation to Weierstrass' $ P$-function


Author: Ulrich Eckhardt
Journal: Math. Comp. 30 (1976), 818-826
MSC: Primary 65D20; Secondary 33A25
DOI: https://doi.org/10.1090/S0025-5718-1976-0421042-0
MathSciNet review: 0421042
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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 $ \vert z\vert < 1/\sqrt 3 $ becomes $ 3 \cdot {10^{ - 14}}$.

The approximation of $ \wp(z)$ is then used to calculate a rational approximation to $ \wp'(z)$ together with an error bound.


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DOI: https://doi.org/10.1090/S0025-5718-1976-0421042-0
Article copyright: © Copyright 1976 American Mathematical Society