Abstract
In this note we derive explicit a priori error bounds for the approximation error and error accumulation of the descending Landen transform. Our results apply to incomplete elliptic integral of the first kind and give the framework to calculate error bounds in the representation of Jacobi's Zeta- and Theta-function.
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Luther, W., Otten, W. Approximation Error and Error Accumulation for the Landen Transform. Reliable Computing 3, 249–258 (1997). https://doi.org/10.1023/A:1009918706545
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DOI: https://doi.org/10.1023/A:1009918706545