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For questions about implementing and using complex arithmetic operations.
6
votes
Numerical computation of the complex elliptic integral $E(k)$ for medium $|k|$
After some searching I found two formulas to solve the accuracy problem.
The two modifications are
In range $|k| \ge 40$ the (asymptotic) series from http://functions.wolfram.com/08.01.06.0010.02 is …
6
votes
1
answer
122
views
Numerical computation of the complex elliptic integral $E(k)$ for medium $|k|$
I have implemented Carlson's algorithm for $E(k)$ from Numerical computation
of real or complex elliptic integrals (available from ArXiv eprint, see
also DLMF). It is essentially his formula (46) whic …