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Jacobi's elliptic functions sn(u|m), cn(u|m), dn(i|m) and φ(u|m) are defined by using the incomplete elliptic integral of the first kind:

JacobianEllipticFunctions subroutine calculates these functions using arithmetic-geometric mean algorithm.
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C# source.
C++ source.
C++ source. MPFR/GMP is used.
GMP source is available from gmplib.org. MPFR source is available from www.mpfr.org.
FreePascal source.
Delphi source.
VBA source.
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