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This paper deals with elliptic integrals of first and second kind and their solution by Landen-transformation. It is explained how the Landen-transformation works and how the different algorithms can be used in geodetic problem solving. The algorithms are recursive and thus easy to implement and stable. Further on the testing is quite simple. The numerical results of the  Landen-transformation are compared to this computed with Maple V to show the exactness of the algorithms. For two algorithms the source-code is depicted.

The derivation of algorithms to compute elliptic integrals of the first and second kind by Landen-transformation