mpmath icon indicating copy to clipboard operation
mpmath copied to clipboard

Jacobi elliptic function for `u = 0`

Open ettersi opened this issue 7 years ago • 0 comments

The Jacobi elliptic functions should satisfy

sn(0,m) == 0
cn(0,m) == 1
dn(0,m) == 1

for any m, see Abramowitz&Stegun, "Handbook of Mathematical Functions", Sec 16.5. This is not the case, however:

mpmath.ellipfun("sn", 0.0, 1.5)   # mpc(real='-1.0052557183770872e-22', imag='8.5907335570440845e-23')
mpmath.ellipfun("cn", 0.0, 1.5)   # mpc(real='1.0', imag='7.0322008877396214e-20')
mpmath.ellipfun("dn", 0.0, 1.5)   # mpc(real='1.0', imag='7.0322008877396214e-20')

Not sure whether this breaks any real code, but it breaks my tests comparing my own code to mpmath. So feel free to leave unanswered.

ettersi avatar Mar 02 '18 18:03 ettersi