sncndn

sncndn, a MATLAB code which evaluates the Jacobi elliptic functions sn(u,m), cn(u,m), and dn(u,m).

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

sncndn is available in a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

sncndn_test

elfun, a MATLAB code which evaluates elliptic integrals, include Bulirsch's integrals cel(), cel1(), cel2(), cel3(), Carlson integrals rc(), rd(), rf(), rg(), rj(), and Jacobi functions cn(), dn(), sn(), by Milan Batista.

elliptic_integral, a MATLAB code which evaluates complete elliptic integrals of first, second and third kind, including the Jacobi elliptic functions sn(), cn(), and dn(), using the Carlson elliptic integral functions.

test_values, a MATLAB code which supplies test values of various mathematical functions, including Abramowitz, AGM, Airy, Bell, Bernoulli, Bessel, Beta, Binomial, Bivariate Normal, Catalan, Cauchy, Chebyshev, Chi Square, Clausen, Clebsch Gordan, Collatz, Cosine integral, Dawson, Debye, Dedekind, dilogarithm, Dixon elliptic functions, Exponential integral, Elliptic, Error, Euler, Exponential integral, F probability, Fresnel, Frobenius, Gamma, Gegenbauer, Goodwin, Gudermannian, Harmonic, Hermite, Hypergeometric 1F1, Hypergeometric 2F1, inverse trigonometic, Jacobi Elliptic functions sn(), cn(), and dn(), the Julian Ephemeris Date, Kelvin, Laguerre, Lambert W, Laplace, Legendre, Lerch, Lobachevsky, Lobatto, Logarithmic integral, Log normal, McNugget numbers, Mertens, Mittag-Leffler, Moebius, Multinomial, Negative binomial, Nine J, Normal, Omega, Owen, Partition, Phi, Pi, Poisson, Polylogarithm, Polynomial Resultant, Polyomino, Prime, Psi, Rayleigh, Hyperbolic Sine integral, Sigma, Sine Power integral, Sine integral, Six J, Sphere area, Sphere volume, Spherical harmonic, Stirling, Stromgen, Struve, Student, Subfactorial, Student probability, Three J, Transport, Trigamma, Truncated normal, van der Corput, von Mises, Weibull, Wright Omega, Zeta.

Reference:

1. Roland Bulirsch,
   Numerical calculation of elliptic integrals and elliptic functions,
   Numerische Mathematik,
   Volume 7, Number 1, 1965, pages 78-90.

Source Code:

• jacobi_cn.m, returns cn(u,m).
• jacobi_cn_values.m, returns selected values of cn(u,m).
• jacobi_dn.m, returns dn(u,m).
• jacobi_dn_values.m, returns selected values of dn(u,m).
• jacobi_sn.m, returns sn(u,m).
• jacobi_sn_values.m, returns selected values of sn(u,m).
• sncndn.m, returns sn(u,m), cn(u,m), dn(u,m).